Inclusion Criteria:

1. Able to understand and sign the informed consent form
2. Age 18 years or older at the time of informed consent
3. Has disease that is measurable by Response Evaluation Criteria in Solid Tumors (RECIST) v.1.1
4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
5. Subjects enrolled in Part 1 and Part 2 dose escalation cohorts must have:

a. Histologically/cytologically confirmed melanoma, triple-negative breast cancer (TNBC), clear cell renal cell cancer (ccRCC), ovarian cancer, head and neck cancer, colorectal cancer, or non-small cell lung cancer (NSCLC) that is metastatic or unresectable with tumor progression after standard therapy who have no options for standard therapies which are known to confer clinical benefit. Subjects with ovarian cancer must have platinum resistant or platinum- refractory tumors.
6. Subjects enrolled in Part 3 and Part 4 dose expansion cohorts must have histologically/cytologically confirmed metastatic or unresectable disease with tumor progression after standard therapy.
7. Adequate organ function defined as follows:

1. Hematology: i. Absolute neutrophil count ≥ 1500 cells/mm3; ii. Platelet count ≥ 75,000 cells/mm3 (without transfusion for 14 days); iii. Hemoglobin ≥ 9 g/dL (and without transfusion within 14 days)
2. Renal: creatinine clearance ≥ 30 mL/min by Cockcroft-Gault estimate
3. Coagulation: Prothrombin time or international normalized ratio and activated partial thromboplastin time ≤ 1.5 × upper limit of normal (ULN) (unless receiving anticoagulation therapy)
4. Hepatic: i. Aspartate aminotransferase and alanine transaminase (ALT) ≤ 3 × ULN (or ≤ 5 × ULN in subjects with known hepatic metastases); ii. Total bilirubin ≤ 1.5 × ULN (isolated value \> 1.5 × ULN is acceptable if direct bilirubin is \< 35% of total)
8. Expected life expectancy of \> 12 weeks per the Investigator
9. Women of childbearing potential (WOCBP) must use a highly effective contraceptive measure (a method that can achieve a failure rate of less than 1% per year) during treatment and until 4 months after the end treatment, such as:

1. Estrogen and progestin containing hormonal contraception that inhibits ovulation
2. Progestin-only hormonal contraception that inhibits ovulation
3. Intrauterine device
4. Vasectomized partner
5. Sexual abstinence
6. Intrauterine hormone-releasing system
7. Bilateral tubal occlusion Note: For WOCBP with breast cancer, alternative non-hormonal contraceptive measures are recommended (c, d, e, g).
10. Potent men that are partners of WOCBP must be willing to use condoms in combination with a second highly effective method of female contraception and agree not to donate sperm from screen through at least 4 months after last dose of study treatment. A male partner will be considered as potent unless surgically sterilized (with appropriate documentation of sterility).

Exclusion Criteria:

1. Active systemic yeast infection within 4 weeks before study treatment
2. Prior hospitalization for asthma during past year
3. Central nervous system metastases except for disease that is asymptomatic, clinically stable, and has not required steroids for at least 28 days before starting study treatment
4. Cardiac disease including:

1. Congestive heart failure New York Heart Association classes II-IV
2. QTcF prolongation \> 480 milliseconds (ms) based on a 12-lead electrocardiogram (ECG)
3. Serious or uncontrolled cardiac arrhythmia within 6 months before starting study treatment
4. Myocardial infarction, unstable angina pectoris, or coronary angioplasty, stenting, or surgery within 6 months before starting study treatment
5. Uncontrolled hypertension (≥ 180 mmHg systolic or ≥ 120 mmHg diastolic)
6. Pericarditis or pericardial effusion that is symptomatic within 6 months before starting study treatment
5. Pulmonary disease including idiopathic pulmonary fibrosis, noninfectious interstitial lung disease, pneumonitis, chronic obstructive pulmonary disease (requiring daily treatment for dyspnea, oxygen therapy on an ongoing basis, or hospitalization within the past 6 months)
6. Hepatic disease resulting in symptomatic ascites, encephalopathy, coagulopathy, esophageal/gastric varices, or persistent jaundice
7. Arterial thrombotic event, stroke, or transient ischemia attack within 6 months before starting study treatment
8. Clinically significant bleeding diathesis or uncontrolled bleeding within 7 days before starting study treatment
9. Bone marrow transplant or solid organ transplant
10. Infection including:

1. Disease requiring systemic therapy within 7 days before starting study treatment
2. Ongoing COVID-19 as determined by viral testing
3. Active human immunodeficiency virus (HIV) infection as determined at screening
4. Active hepatitis B infection as determined at screening
5. Active hepatitis C infection as determined at screening
11. Autoimmune disease requiring systemic disease-modifying or immunosuppressive therapy within 2 years before starting study treatment. Exceptions include disease managed with only replacement therapies (eg, thyroxine, etc.)
12. History of hemophagocytic lymphohistiocytosis/macrophage activation syndrome
13. Malignancy within 2 years before starting study treatment other than the disease under study. Exceptions include indolent or definitively treated disease not expected to require treatment during the study, affect the safety of subjects, or affect the endpoints of the trial
14. Any medical condition requiring corticosteroids (\> 10 mg daily oral prednisone or equivalent) or other systemic immunosuppressive therapy within 28 days before starting study treatment. Exception: Intermittent or sporadic use of inhaled or topical steroids is allowed
15. Residual toxicity from previous treatment including:

1. Toxicity related to prior treatment not resolved to Grade 1, except for alopecia or dysgeusia
2. Neuropathy Grade \> 2 Note: Exceptions to the above criteria include toxicities that do not pose a risk to vital organ systems (eg, alopecia) or toxicities that are stable as managed by replacement therapies (eg, hypothyroidism)
16. Subjects receiving cemiplimab: those that have permanently discontinued immuno- modulating therapies due to drug-related toxicity.
17. Subjects receiving cemiplimab: hypersensitivity to cemiplimab or any of its excipients or contraindicated to cemiplimab per approved local labeling
18. Any investigational agent within 28 days before starting study treatment or within 5 estimated elimination half-lives, whichever is shorter
19. Radiation therapy within 14 days before starting study treatment
20. History of severe hypersensitivity to any ingredient of BDC-3042 or study treatment (as applicable for combination study treatment)
21. Received live/attenuated virus vaccine within 28 days before starting study treatment
22. Major surgery within 28 days of starting study treatment (consult with Medical Monitor)
23. Actively enrolled in another clinical study, unless it is an observational (noninterventional) clinical study or the follow-up component of an interventional study
24. Patient is a lactating mother or pregnant as confirmed by pregnancy tests within 7 days prior to start of study treatment
25. Patient is unwilling or unable to follow protocol requirements
26. Ongoing bowel perforation or presence of bowel fistula or intra-abdominal abscess
27. Any condition that, in the opinion of the Investigator, would interfere with evaluation of BDC-3042 or interpretation of the patient's safety or study results

Inclusion Criteria:

1. Able to understand and sign the informed consent form
2. Age 18 years or older at the time of informed consent
3. Has disease that is measurable by Response Evaluation Criteria in Solid Tumors (RECIST) v.1.1
4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
5. Subjects enrolled in Part 1 and Part 2 dose escalation cohorts must have:

a. Histologically/cytologically confirmed melanoma, triple-negative breast cancer (TNBC), clear cell renal cell cancer (ccRCC), ovarian cancer, head and neck cancer, colorectal cancer, or non-small cell lung cancer (NSCLC) that is metastatic or unresectable with tumor progression after standard therapy who have no options for standard therapies which are known to confer clinical benefit. Subjects with ovarian cancer must have platinum resistant or platinum- refractory tumors.
6. Subjects enrolled in Part 3 and Part 4 dose expansion cohorts must have histologically/cytologically confirmed metastatic or unresectable disease with tumor progression after standard therapy.
7. Adequate organ function defined as follows:

1. Hematology: i. Absolute neutrophil count ≥ 1500 cells/mm3; ii. Platelet count ≥ 75,000 cells/mm3 (without transfusion for 14 days); iii. Hemoglobin ≥ 9 g/dL (and without transfusion within 14 days)
2. Renal: creatinine clearance ≥ 30 mL/min by Cockcroft-Gault estimate
3. Coagulation: Prothrombin time or international normalized ratio and activated partial thromboplastin time ≤ 1.5 × upper limit of normal (ULN) (unless receiving anticoagulation therapy)
4. Hepatic: i. Aspartate aminotransferase and alanine transaminase (ALT) ≤ 3 × ULN (or ≤ 5 × ULN in subjects with known hepatic metastases); ii. Total bilirubin ≤ 1.5 × ULN (isolated value \> 1.5 × ULN is acceptable if direct bilirubin is \< 35% of total)
8. Expected life expectancy of \> 12 weeks per the Investigator
9. Women of childbearing potential (WOCBP) must use a highly effective contraceptive measure (a method that can achieve a failure rate of less than 1% per year) during treatment and until 4 months after the end treatment, such as:

1. Estrogen and progestin containing hormonal contraception that inhibits ovulation
2. Progestin-only hormonal contraception that inhibits ovulation
3. Intrauterine device
4. Vasectomized partner
5. Sexual abstinence
6. Intrauterine hormone-releasing system
7. Bilateral tubal occlusion Note: For WOCBP with breast cancer, alternative non-hormonal contraceptive measures are recommended (c, d, e, g).
10. Potent men that are partners of WOCBP must be willing to use condoms in combination with a second highly effective method of female contraception and agree not to donate sperm from screen through at least 4 months after last dose of study treatment. A male partner will be considered as potent unless surgically sterilized (with appropriate documentation of sterility).

Exclusion Criteria:

1. Active systemic yeast infection within 4 weeks before study treatment
2. Prior hospitalization for asthma during past year
3. Central nervous system metastases except for disease that is asymptomatic, clinically stable, and has not required steroids for at least 28 days before starting study treatment
4. Cardiac disease including:

1. Congestive heart failure New York Heart Association classes II-IV
2. QTcF prolongation \> 480 milliseconds (ms) based on a 12-lead electrocardiogram (ECG)
3. Serious or uncontrolled cardiac arrhythmia within 6 months before starting study treatment
4. Myocardial infarction, unstable angina pectoris, or coronary angioplasty, stenting, or surgery within 6 months before starting study treatment
5. Uncontrolled hypertension (≥ 180 mmHg systolic or ≥ 120 mmHg diastolic)
6. Pericarditis or pericardial effusion that is symptomatic within 6 months before starting study treatment
5. Pulmonary disease including idiopathic pulmonary fibrosis, noninfectious interstitial lung disease, pneumonitis, chronic obstructive pulmonary disease (requiring daily treatment for dyspnea, oxygen therapy on an ongoing basis, or hospitalization within the past 6 months)
6. Hepatic disease resulting in symptomatic ascites, encephalopathy, coagulopathy, esophageal/gastric varices, or persistent jaundice
7. Arterial thrombotic event, stroke, or transient ischemia attack within 6 months before starting study treatment
8. Clinically significant bleeding diathesis or uncontrolled bleeding within 7 days before starting study treatment
9. Bone marrow transplant or solid organ transplant
10. Infection including:

1. Disease requiring systemic therapy within 7 days before starting study treatment
2. Ongoing COVID-19 as determined by viral testing
3. Active human immunodeficiency virus (HIV) infection as determined at screening
4. Active hepatitis B infection as determined at screening
5. Active hepatitis C infection as determined at screening
11. Autoimmune disease requiring systemic disease-modifying or immunosuppressive therapy within 2 years before starting study treatment. Exceptions include disease managed with only replacement therapies (eg, thyroxine, etc.)
12. History of hemophagocytic lymphohistiocytosis/macrophage activation syndrome
13. Malignancy within 2 years before starting study treatment other than the disease under study. Exceptions include indolent or definitively treated disease not expected to require treatment during the study, affect the safety of subjects, or affect the endpoints of the trial
14. Any medical condition requiring corticosteroids (\> 10 mg daily oral prednisone or equivalent) or other systemic immunosuppressive therapy within 28 days before starting study treatment. Exception: Intermittent or sporadic use of inhaled or topical steroids is allowed
15. Residual toxicity from previous treatment including:

1. Toxicity related to prior treatment not resolved to Grade 1, except for alopecia or dysgeusia
2. Neuropathy Grade \> 2 Note: Exceptions to the above criteria include toxicities that do not pose a risk to vital organ systems (eg, alopecia) or toxicities that are stable as managed by replacement therapies (eg, hypothyroidism)
16. Subjects receiving cemiplimab: those that have permanently discontinued immuno- modulating therapies due to drug-related toxicity.
17. Subjects receiving cemiplimab: hypersensitivity to cemiplimab or any of its excipients or contraindicated to cemiplimab per approved local labeling
18. Any investigational agent within 28 days before starting study treatment or within 5 estimated elimination half-lives, whichever is shorter
19. Radiation therapy within 14 days before starting study treatment
20. History of severe hypersensitivity to any ingredient of BDC-3042 or study treatment (as applicable for combination study treatment)
21. Received live/attenuated virus vaccine within 28 days before starting study treatment
22. Major surgery within 28 days of starting study treatment (consult with Medical Monitor)
23. Actively enrolled in another clinical study, unless it is an observational (noninterventional) clinical study or the follow-up component of an interventional study
24. Patient is a lactating mother or pregnant as confirmed by pregnancy tests within 7 days prior to start of study treatment
25. Patient is unwilling or unable to follow protocol requirements
26. Ongoing bowel perforation or presence of bowel fistula or intra-abdominal abscess
27. Any condition that, in the opinion of the Investigator, would interfere with evaluation of BDC-3042 or interpretation of the patient's safety or study results

Inclusion Criteria:

1. Able to understand and sign the informed consent form
2. Age 18 years or older at the time of informed consent
3. Has disease that is measurable by Response Evaluation Criteria in Solid Tumors (RECIST) v.1.1
4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
5. Subjects enrolled in Part 1 and Part 2 dose escalation cohorts must have:

a. Histologically/cytologically confirmed melanoma, triple-negative breast cancer (TNBC), clear cell renal cell cancer (ccRCC), ovarian cancer, head and neck cancer, colorectal cancer, or non-small cell lung cancer (NSCLC) that is metastatic or unresectable with tumor progression after standard therapy who have no options for standard therapies which are known to confer clinical benefit. Subjects with ovarian cancer must have platinum resistant or platinum- refractory tumors.
6. Subjects enrolled in Part 3 and Part 4 dose expansion cohorts must have histologically/cytologically confirmed metastatic or unresectable disease with tumor progression after standard therapy.
7. Adequate organ function defined as follows:

1. Hematology: i. Absolute neutrophil count ≥ 1500 cells/mm3; ii. Platelet count ≥ 75,000 cells/mm3 (without transfusion for 14 days); iii. Hemoglobin ≥ 9 g/dL (and without transfusion within 14 days)
2. Renal: creatinine clearance ≥ 30 mL/min by Cockcroft-Gault estimate
3. Coagulation: Prothrombin time or international normalized ratio and activated partial thromboplastin time ≤ 1.5 × upper limit of normal (ULN) (unless receiving anticoagulation therapy)
4. Hepatic: i. Aspartate aminotransferase and alanine transaminase (ALT) ≤ 3 × ULN (or ≤ 5 × ULN in subjects with known hepatic metastases); ii. Total bilirubin ≤ 1.5 × ULN (isolated value \> 1.5 × ULN is acceptable if direct bilirubin is \< 35% of total)
8. Expected life expectancy of \> 12 weeks per the Investigator
9. Women of childbearing potential (WOCBP) must use a highly effective contraceptive measure (a method that can achieve a failure rate of less than 1% per year) during treatment and until 4 months after the end treatment, such as:

1. Estrogen and progestin containing hormonal contraception that inhibits ovulation
2. Progestin-only hormonal contraception that inhibits ovulation
3. Intrauterine device
4. Vasectomized partner
5. Sexual abstinence
6. Intrauterine hormone-releasing system
7. Bilateral tubal occlusion Note: For WOCBP with breast cancer, alternative non-hormonal contraceptive measures are recommended (c, d, e, g).
10. Potent men that are partners of WOCBP must be willing to use condoms in combination with a second highly effective method of female contraception and agree not to donate sperm from screen through at least 4 months after last dose of study treatment. A male partner will be considered as potent unless surgically sterilized (with appropriate documentation of sterility).

Exclusion Criteria:

1. Active systemic yeast infection within 4 weeks before study treatment
2. Prior hospitalization for asthma during past year
3. Central nervous system metastases except for disease that is asymptomatic, clinically stable, and has not required steroids for at least 28 days before starting study treatment
4. Cardiac disease including:

1. Congestive heart failure New York Heart Association classes II-IV
2. QTcF prolongation \> 480 milliseconds (ms) based on a 12-lead electrocardiogram (ECG)
3. Serious or uncontrolled cardiac arrhythmia within 6 months before starting study treatment
4. Myocardial infarction, unstable angina pectoris, or coronary angioplasty, stenting, or surgery within 6 months before starting study treatment
5. Uncontrolled hypertension (≥ 180 mmHg systolic or ≥ 120 mmHg diastolic)
6. Pericarditis or pericardial effusion that is symptomatic within 6 months before starting study treatment
5. Pulmonary disease including idiopathic pulmonary fibrosis, noninfectious interstitial lung disease, pneumonitis, chronic obstructive pulmonary disease (requiring daily treatment for dyspnea, oxygen therapy on an ongoing basis, or hospitalization within the past 6 months)
6. Hepatic disease resulting in symptomatic ascites, encephalopathy, coagulopathy, esophageal/gastric varices, or persistent jaundice
7. Arterial thrombotic event, stroke, or transient ischemia attack within 6 months before starting study treatment
8. Clinically significant bleeding diathesis or uncontrolled bleeding within 7 days before starting study treatment
9. Bone marrow transplant or solid organ transplant
10. Infection including:

1. Disease requiring systemic therapy within 7 days before starting study treatment
2. Ongoing COVID-19 as determined by viral testing
3. Active human immunodeficiency virus (HIV) infection as determined at screening
4. Active hepatitis B infection as determined at screening
5. Active hepatitis C infection as determined at screening
11. Autoimmune disease requiring systemic disease-modifying or immunosuppressive therapy within 2 years before starting study treatment. Exceptions include disease managed with only replacement therapies (eg, thyroxine, etc.)
12. History of hemophagocytic lymphohistiocytosis/macrophage activation syndrome
13. Malignancy within 2 years before starting study treatment other than the disease under study. Exceptions include indolent or definitively treated disease not expected to require treatment during the study, affect the safety of subjects, or affect the endpoints of the trial
14. Any medical condition requiring corticosteroids (\> 10 mg daily oral prednisone or equivalent) or other systemic immunosuppressive therapy within 28 days before starting study treatment. Exception: Intermittent or sporadic use of inhaled or topical steroids is allowed
15. Residual toxicity from previous treatment including:

1. Toxicity related to prior treatment not resolved to Grade 1, except for alopecia or dysgeusia
2. Neuropathy Grade \> 2 Note: Exceptions to the above criteria include toxicities that do not pose a risk to vital organ systems (eg, alopecia) or toxicities that are stable as managed by replacement therapies (eg, hypothyroidism)
16. Subjects receiving cemiplimab: those that have permanently discontinued immuno- modulating therapies due to drug-related toxicity.
17. Subjects receiving cemiplimab: hypersensitivity to cemiplimab or any of its excipients or contraindicated to cemiplimab per approved local labeling
18. Any investigational agent within 28 days before starting study treatment or within 5 estimated elimination half-lives, whichever is shorter
19. Radiation therapy within 14 days before starting study treatment
20. History of severe hypersensitivity to any ingredient of BDC-3042 or study treatment (as applicable for combination study treatment)
21. Received live/attenuated virus vaccine within 28 days before starting study treatment
22. Major surgery within 28 days of starting study treatment (consult with Medical Monitor)
23. Actively enrolled in another clinical study, unless it is an observational (noninterventional) clinical study or the follow-up component of an interventional study
24. Patient is a lactating mother or pregnant as confirmed by pregnancy tests within 7 days prior to start of study treatment
25. Patient is unwilling or unable to follow protocol requirements
26. Ongoing bowel perforation or presence of bowel fistula or intra-abdominal abscess
27. Any condition that, in the opinion of the Investigator, would interfere with evaluation of BDC-3042 or interpretation of the patient's safety or study results

Inclusion Criteria:

1. Able to understand and sign the informed consent form
2. Age 18 years or older at the time of informed consent
3. Has disease that is measurable by Response Evaluation Criteria in Solid Tumors (RECIST) v.1.1
4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
5. Subjects enrolled in Part 1 and Part 2 dose escalation cohorts must have:

a. Histologically/cytologically confirmed melanoma, triple-negative breast cancer (TNBC), clear cell renal cell cancer (ccRCC), ovarian cancer, head and neck cancer, colorectal cancer, or non-small cell lung cancer (NSCLC) that is metastatic or unresectable with tumor progression after standard therapy who have no options for standard therapies which are known to confer clinical benefit. Subjects with ovarian cancer must have platinum resistant or platinum- refractory tumors.
6. Subjects enrolled in Part 3 and Part 4 dose expansion cohorts must have histologically/cytologically confirmed metastatic or unresectable disease with tumor progression after standard therapy.
7. Adequate organ function defined as follows:

1. Hematology: i. Absolute neutrophil count ≥ 1500 cells/mm3; ii. Platelet count ≥ 75,000 cells/mm3 (without transfusion for 14 days); iii. Hemoglobin ≥ 9 g/dL (and without transfusion within 14 days)
2. Renal: creatinine clearance ≥ 30 mL/min by Cockcroft-Gault estimate
3. Coagulation: Prothrombin time or international normalized ratio and activated partial thromboplastin time ≤ 1.5 × upper limit of normal (ULN) (unless receiving anticoagulation therapy)
4. Hepatic: i. Aspartate aminotransferase and alanine transaminase (ALT) ≤ 3 × ULN (or ≤ 5 × ULN in subjects with known hepatic metastases); ii. Total bilirubin ≤ 1.5 × ULN (isolated value \> 1.5 × ULN is acceptable if direct bilirubin is \< 35% of total)
8. Expected life expectancy of \> 12 weeks per the Investigator
9. Women of childbearing potential (WOCBP) must use a highly effective contraceptive measure (a method that can achieve a failure rate of less than 1% per year) during treatment and until 4 months after the end treatment, such as:

1. Estrogen and progestin containing hormonal contraception that inhibits ovulation
2. Progestin-only hormonal contraception that inhibits ovulation
3. Intrauterine device
4. Vasectomized partner
5. Sexual abstinence
6. Intrauterine hormone-releasing system
7. Bilateral tubal occlusion Note: For WOCBP with breast cancer, alternative non-hormonal contraceptive measures are recommended (c, d, e, g).
10. Potent men that are partners of WOCBP must be willing to use condoms in combination with a second highly effective method of female contraception and agree not to donate sperm from screen through at least 4 months after last dose of study treatment. A male partner will be considered as potent unless surgically sterilized (with appropriate documentation of sterility).

Exclusion Criteria:

1. Active systemic yeast infection within 4 weeks before study treatment
2. Prior hospitalization for asthma during past year
3. Central nervous system metastases except for disease that is asymptomatic, clinically stable, and has not required steroids for at least 28 days before starting study treatment
4. Cardiac disease including:

1. Congestive heart failure New York Heart Association classes II-IV
2. QTcF prolongation \> 480 milliseconds (ms) based on a 12-lead electrocardiogram (ECG)
3. Serious or uncontrolled cardiac arrhythmia within 6 months before starting study treatment
4. Myocardial infarction, unstable angina pectoris, or coronary angioplasty, stenting, or surgery within 6 months before starting study treatment
5. Uncontrolled hypertension (≥ 180 mmHg systolic or ≥ 120 mmHg diastolic)
6. Pericarditis or pericardial effusion that is symptomatic within 6 months before starting study treatment
5. Pulmonary disease including idiopathic pulmonary fibrosis, noninfectious interstitial lung disease, pneumonitis, chronic obstructive pulmonary disease (requiring daily treatment for dyspnea, oxygen therapy on an ongoing basis, or hospitalization within the past 6 months)
6. Hepatic disease resulting in symptomatic ascites, encephalopathy, coagulopathy, esophageal/gastric varices, or persistent jaundice
7. Arterial thrombotic event, stroke, or transient ischemia attack within 6 months before starting study treatment
8. Clinically significant bleeding diathesis or uncontrolled bleeding within 7 days before starting study treatment
9. Bone marrow transplant or solid organ transplant
10. Infection including:

1. Disease requiring systemic therapy within 7 days before starting study treatment
2. Ongoing COVID-19 as determined by viral testing
3. Active human immunodeficiency virus (HIV) infection as determined at screening
4. Active hepatitis B infection as determined at screening
5. Active hepatitis C infection as determined at screening
11. Autoimmune disease requiring systemic disease-modifying or immunosuppressive therapy within 2 years before starting study treatment. Exceptions include disease managed with only replacement therapies (eg, thyroxine, etc.)
12. History of hemophagocytic lymphohistiocytosis/macrophage activation syndrome
13. Malignancy within 2 years before starting study treatment other than the disease under study. Exceptions include indolent or definitively treated disease not expected to require treatment during the study, affect the safety of subjects, or affect the endpoints of the trial
14. Any medical condition requiring corticosteroids (\> 10 mg daily oral prednisone or equivalent) or other systemic immunosuppressive therapy within 28 days before starting study treatment. Exception: Intermittent or sporadic use of inhaled or topical steroids is allowed
15. Residual toxicity from previous treatment including:

1. Toxicity related to prior treatment not resolved to Grade 1, except for alopecia or dysgeusia
2. Neuropathy Grade \> 2 Note: Exceptions to the above criteria include toxicities that do not pose a risk to vital organ systems (eg, alopecia) or toxicities that are stable as managed by replacement therapies (eg, hypothyroidism)
16. Subjects receiving cemiplimab: those that have permanently discontinued immuno- modulating therapies due to drug-related toxicity.
17. Subjects receiving cemiplimab: hypersensitivity to cemiplimab or any of its excipients or contraindicated to cemiplimab per approved local labeling
18. Any investigational agent within 28 days before starting study treatment or within 5 estimated elimination half-lives, whichever is shorter
19. Radiation therapy within 14 days before starting study treatment
20. History of severe hypersensitivity to any ingredient of BDC-3042 or study treatment (as applicable for combination study treatment)
21. Received live/attenuated virus vaccine within 28 days before starting study treatment
22. Major surgery within 28 days of starting study treatment (consult with Medical Monitor)
23. Actively enrolled in another clinical study, unless it is an observational (noninterventional) clinical study or the follow-up component of an interventional study
24. Patient is a lactating mother or pregnant as confirmed by pregnancy tests within 7 days prior to start of study treatment
25. Patient is unwilling or unable to follow protocol requirements
26. Ongoing bowel perforation or presence of bowel fistula or intra-abdominal abscess
27. Any condition that, in the opinion of the Investigator, would interfere with evaluation of BDC-3042 or interpretation of the patient's safety or study results

Inclusion Criteria:

1. Able to understand and sign the informed consent form
2. Age 18 years or older at the time of informed consent
3. Has disease that is measurable by Response Evaluation Criteria in Solid Tumors (RECIST) v.1.1
4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
5. Subjects enrolled in Part 1 and Part 2 dose escalation cohorts must have:

a. Histologically/cytologically confirmed melanoma, triple-negative breast cancer (TNBC), clear cell renal cell cancer (ccRCC), ovarian cancer, head and neck cancer, colorectal cancer, or non-small cell lung cancer (NSCLC) that is metastatic or unresectable with tumor progression after standard therapy who have no options for standard therapies which are known to confer clinical benefit. Subjects with ovarian cancer must have platinum resistant or platinum- refractory tumors.
6. Subjects enrolled in Part 3 and Part 4 dose expansion cohorts must have histologically/cytologically confirmed metastatic or unresectable disease with tumor progression after standard therapy.
7. Adequate organ function defined as follows:

1. Hematology: i. Absolute neutrophil count ≥ 1500 cells/mm3; ii. Platelet count ≥ 75,000 cells/mm3 (without transfusion for 14 days); iii. Hemoglobin ≥ 9 g/dL (and without transfusion within 14 days)
2. Renal: creatinine clearance ≥ 30 mL/min by Cockcroft-Gault estimate
3. Coagulation: Prothrombin time or international normalized ratio and activated partial thromboplastin time ≤ 1.5 × upper limit of normal (ULN) (unless receiving anticoagulation therapy)
4. Hepatic: i. Aspartate aminotransferase and alanine transaminase (ALT) ≤ 3 × ULN (or ≤ 5 × ULN in subjects with known hepatic metastases); ii. Total bilirubin ≤ 1.5 × ULN (isolated value \> 1.5 × ULN is acceptable if direct bilirubin is \< 35% of total)
8. Expected life expectancy of \> 12 weeks per the Investigator
9. Women of childbearing potential (WOCBP) must use a highly effective contraceptive measure (a method that can achieve a failure rate of less than 1% per year) during treatment and until 4 months after the end treatment, such as:

1. Estrogen and progestin containing hormonal contraception that inhibits ovulation
2. Progestin-only hormonal contraception that inhibits ovulation
3. Intrauterine device
4. Vasectomized partner
5. Sexual abstinence
6. Intrauterine hormone-releasing system
7. Bilateral tubal occlusion Note: For WOCBP with breast cancer, alternative non-hormonal contraceptive measures are recommended (c, d, e, g).
10. Potent men that are partners of WOCBP must be willing to use condoms in combination with a second highly effective method of female contraception and agree not to donate sperm from screen through at least 4 months after last dose of study treatment. A male partner will be considered as potent unless surgically sterilized (with appropriate documentation of sterility).

Exclusion Criteria:

1. Active systemic yeast infection within 4 weeks before study treatment
2. Prior hospitalization for asthma during past year
3. Central nervous system metastases except for disease that is asymptomatic, clinically stable, and has not required steroids for at least 28 days before starting study treatment
4. Cardiac disease including:

1. Congestive heart failure New York Heart Association classes II-IV
2. QTcF prolongation \> 480 milliseconds (ms) based on a 12-lead electrocardiogram (ECG)
3. Serious or uncontrolled cardiac arrhythmia within 6 months before starting study treatment
4. Myocardial infarction, unstable angina pectoris, or coronary angioplasty, stenting, or surgery within 6 months before starting study treatment
5. Uncontrolled hypertension (≥ 180 mmHg systolic or ≥ 120 mmHg diastolic)
6. Pericarditis or pericardial effusion that is symptomatic within 6 months before starting study treatment
5. Pulmonary disease including idiopathic pulmonary fibrosis, noninfectious interstitial lung disease, pneumonitis, chronic obstructive pulmonary disease (requiring daily treatment for dyspnea, oxygen therapy on an ongoing basis, or hospitalization within the past 6 months)
6. Hepatic disease resulting in symptomatic ascites, encephalopathy, coagulopathy, esophageal/gastric varices, or persistent jaundice
7. Arterial thrombotic event, stroke, or transient ischemia attack within 6 months before starting study treatment
8. Clinically significant bleeding diathesis or uncontrolled bleeding within 7 days before starting study treatment
9. Bone marrow transplant or solid organ transplant
10. Infection including:

1. Disease requiring systemic therapy within 7 days before starting study treatment
2. Ongoing COVID-19 as determined by viral testing
3. Active human immunodeficiency virus (HIV) infection as determined at screening
4. Active hepatitis B infection as determined at screening
5. Active hepatitis C infection as determined at screening
11. Autoimmune disease requiring systemic disease-modifying or immunosuppressive therapy within 2 years before starting study treatment. Exceptions include disease managed with only replacement therapies (eg, thyroxine, etc.)
12. History of hemophagocytic lymphohistiocytosis/macrophage activation syndrome
13. Malignancy within 2 years before starting study treatment other than the disease under study. Exceptions include indolent or definitively treated disease not expected to require treatment during the study, affect the safety of subjects, or affect the endpoints of the trial
14. Any medical condition requiring corticosteroids (\> 10 mg daily oral prednisone or equivalent) or other systemic immunosuppressive therapy within 28 days before starting study treatment. Exception: Intermittent or sporadic use of inhaled or topical steroids is allowed
15. Residual toxicity from previous treatment including:

1. Toxicity related to prior treatment not resolved to Grade 1, except for alopecia or dysgeusia
2. Neuropathy Grade \> 2 Note: Exceptions to the above criteria include toxicities that do not pose a risk to vital organ systems (eg, alopecia) or toxicities that are stable as managed by replacement therapies (eg, hypothyroidism)
16. Subjects receiving cemiplimab: those that have permanently discontinued immuno- modulating therapies due to drug-related toxicity.
17. Subjects receiving cemiplimab: hypersensitivity to cemiplimab or any of its excipients or contraindicated to cemiplimab per approved local labeling
18. Any investigational agent within 28 days before starting study treatment or within 5 estimated elimination half-lives, whichever is shorter
19. Radiation therapy within 14 days before starting study treatment
20. History of severe hypersensitivity to any ingredient of BDC-3042 or study treatment (as applicable for combination study treatment)
21. Received live/attenuated virus vaccine within 28 days before starting study treatment
22. Major surgery within 28 days of starting study treatment (consult with Medical Monitor)
23. Actively enrolled in another clinical study, unless it is an observational (noninterventional) clinical study or the follow-up component of an interventional study
24. Patient is a lactating mother or pregnant as confirmed by pregnancy tests within 7 days prior to start of study treatment
25. Patient is unwilling or unable to follow protocol requirements
26. Ongoing bowel perforation or presence of bowel fistula or intra-abdominal abscess
27. Any condition that, in the opinion of the Investigator, would interfere with evaluation of BDC-3042 or interpretation of the patient's safety or study results

Inclusion Criteria:

1. Able to understand and sign the informed consent form
2. Age 18 years or older at the time of informed consent
3. Has disease that is measurable by Response Evaluation Criteria in Solid Tumors (RECIST) v.1.1
4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
5. Subjects enrolled in Part 1 and Part 2 dose escalation cohorts must have:

a. Histologically/cytologically confirmed melanoma, triple-negative breast cancer (TNBC), clear cell renal cell cancer (ccRCC), ovarian cancer, head and neck cancer, colorectal cancer, or non-small cell lung cancer (NSCLC) that is metastatic or unresectable with tumor progression after standard therapy who have no options for standard therapies which are known to confer clinical benefit. Subjects with ovarian cancer must have platinum resistant or platinum- refractory tumors.
6. Subjects enrolled in Part 3 and Part 4 dose expansion cohorts must have histologically/cytologically confirmed metastatic or unresectable disease with tumor progression after standard therapy.
7. Adequate organ function defined as follows:

1. Hematology: i. Absolute neutrophil count ≥ 1500 cells/mm3; ii. Platelet count ≥ 75,000 cells/mm3 (without transfusion for 14 days); iii. Hemoglobin ≥ 9 g/dL (and without transfusion within 14 days)
2. Renal: creatinine clearance ≥ 30 mL/min by Cockcroft-Gault estimate
3. Coagulation: Prothrombin time or international normalized ratio and activated partial thromboplastin time ≤ 1.5 × upper limit of normal (ULN) (unless receiving anticoagulation therapy)
4. Hepatic: i. Aspartate aminotransferase and alanine transaminase (ALT) ≤ 3 × ULN (or ≤ 5 × ULN in subjects with known hepatic metastases); ii. Total bilirubin ≤ 1.5 × ULN (isolated value \> 1.5 × ULN is acceptable if direct bilirubin is \< 35% of total)
8. Expected life expectancy of \> 12 weeks per the Investigator
9. Women of childbearing potential (WOCBP) must use a highly effective contraceptive measure (a method that can achieve a failure rate of less than 1% per year) during treatment and until 4 months after the end treatment, such as:

1. Estrogen and progestin containing hormonal contraception that inhibits ovulation
2. Progestin-only hormonal contraception that inhibits ovulation
3. Intrauterine device
4. Vasectomized partner
5. Sexual abstinence
6. Intrauterine hormone-releasing system
7. Bilateral tubal occlusion Note: For WOCBP with breast cancer, alternative non-hormonal contraceptive measures are recommended (c, d, e, g).
10. Potent men that are partners of WOCBP must be willing to use condoms in combination with a second highly effective method of female contraception and agree not to donate sperm from screen through at least 4 months after last dose of study treatment. A male partner will be considered as potent unless surgically sterilized (with appropriate documentation of sterility).

Exclusion Criteria:

1. Active systemic yeast infection within 4 weeks before study treatment
2. Prior hospitalization for asthma during past year
3. Central nervous system metastases except for disease that is asymptomatic, clinically stable, and has not required steroids for at least 28 days before starting study treatment
4. Cardiac disease including:

1. Congestive heart failure New York Heart Association classes II-IV
2. QTcF prolongation \> 480 milliseconds (ms) based on a 12-lead electrocardiogram (ECG)
3. Serious or uncontrolled cardiac arrhythmia within 6 months before starting study treatment
4. Myocardial infarction, unstable angina pectoris, or coronary angioplasty, stenting, or surgery within 6 months before starting study treatment
5. Uncontrolled hypertension (≥ 180 mmHg systolic or ≥ 120 mmHg diastolic)
6. Pericarditis or pericardial effusion that is symptomatic within 6 months before starting study treatment
5. Pulmonary disease including idiopathic pulmonary fibrosis, noninfectious interstitial lung disease, pneumonitis, chronic obstructive pulmonary disease (requiring daily treatment for dyspnea, oxygen therapy on an ongoing basis, or hospitalization within the past 6 months)
6. Hepatic disease resulting in symptomatic ascites, encephalopathy, coagulopathy, esophageal/gastric varices, or persistent jaundice
7. Arterial thrombotic event, stroke, or transient ischemia attack within 6 months before starting study treatment
8. Clinically significant bleeding diathesis or uncontrolled bleeding within 7 days before starting study treatment
9. Bone marrow transplant or solid organ transplant
10. Infection including:

1. Disease requiring systemic therapy within 7 days before starting study treatment
2. Ongoing COVID-19 as determined by viral testing
3. Active human immunodeficiency virus (HIV) infection as determined at screening
4. Active hepatitis B infection as determined at screening
5. Active hepatitis C infection as determined at screening
11. Autoimmune disease requiring systemic disease-modifying or immunosuppressive therapy within 2 years before starting study treatment. Exceptions include disease managed with only replacement therapies (eg, thyroxine, etc.)
12. History of hemophagocytic lymphohistiocytosis/macrophage activation syndrome
13. Malignancy within 2 years before starting study treatment other than the disease under study. Exceptions include indolent or definitively treated disease not expected to require treatment during the study, affect the safety of subjects, or affect the endpoints of the trial
14. Any medical condition requiring corticosteroids (\> 10 mg daily oral prednisone or equivalent) or other systemic immunosuppressive therapy within 28 days before starting study treatment. Exception: Intermittent or sporadic use of inhaled or topical steroids is allowed
15. Residual toxicity from previous treatment including:

1. Toxicity related to prior treatment not resolved to Grade 1, except for alopecia or dysgeusia
2. Neuropathy Grade \> 2 Note: Exceptions to the above criteria include toxicities that do not pose a risk to vital organ systems (eg, alopecia) or toxicities that are stable as managed by replacement therapies (eg, hypothyroidism)
16. Subjects receiving cemiplimab: those that have permanently discontinued immuno- modulating therapies due to drug-related toxicity.
17. Subjects receiving cemiplimab: hypersensitivity to cemiplimab or any of its excipients or contraindicated to cemiplimab per approved local labeling
18. Any investigational agent within 28 days before starting study treatment or within 5 estimated elimination half-lives, whichever is shorter
19. Radiation therapy within 14 days before starting study treatment
20. History of severe hypersensitivity to any ingredient of BDC-3042 or study treatment (as applicable for combination study treatment)
21. Received live/attenuated virus vaccine within 28 days before starting study treatment
22. Major surgery within 28 days of starting study treatment (consult with Medical Monitor)
23. Actively enrolled in another clinical study, unless it is an observational (noninterventional) clinical study or the follow-up component of an interventional study
24. Patient is a lactating mother or pregnant as confirmed by pregnancy tests within 7 days prior to start of study treatment
25. Patient is unwilling or unable to follow protocol requirements
26. Ongoing bowel perforation or presence of bowel fistula or intra-abdominal abscess
27. Any condition that, in the opinion of the Investigator, would interfere with evaluation of BDC-3042 or interpretation of the patient's safety or study results