Inclusion Criteria:

   - STEP 1 REGISTRATION AND RANDOMIZATION

   - Patients must be >= 18 years of age

   - Patient must have the ability to understand and the willingness to sign a written
   informed consent document. Patients with impaired decision-making capacity (IDMC) who
   have a legally authorized representative (LAR) or caregiver and/or family member
   available will also be considered eligible

   - Patient must have a diagnosis of high grade upper tract urothelial carcinoma proven by
   biopsy within 12 weeks (84 days) prior to registration/randomization with one of the
   following:

      - Upper urinary tract mass on cross-sectional imaging or

      - Tumor directly visualized during upper urinary tract endoscopy before referral to
      medical oncology

         - NOTE: Biopsy is standard of care (SOC) and required for enrollment to study.
         This is vital for best practice

   - Leukocytes >= 3,000/mcL (obtained =< 14 days prior to registration/randomization)

   - Platelets >= 100,000/mcL (obtained =< 14 days prior to registration/randomization)

   - Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (or =< 2.5 x ULN
   for patients with Gilbert's disease) (obtained =< 14 days prior to
   registration/randomization)

   - Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
   [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
   =< 2.5 x institutional ULN (obtained =< 14 days prior to registration/randomization)

   - Hemoglobin (Hgb) >= 9 g/dL (obtained =< 14 days prior to registration/randomization)

      - NOTE: Packed red blood transfusion is allowed to achieve this parameter as per
      treating investigator

   - Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral
   therapy with undetectable viral load within 6 months prior to
   registration/randomization are eligible for this trial

      - NOTE: These patients must be stable on their anti-retroviral regimen with
      evidence of at least two undetectable viral loads within the past 6 months on the
      same regimen; the most recent undetectable viral load must be within the past 12
      weeks. They must have a CD4 count of greater than 250 cells/mcL over the past 6
      months on this same anti-retroviral regimen and must not have had a CD4 count <
      200 cells/mcL over the past 2 years, unless it was deemed related to the cancer
      and/or chemotherapy induced bone marrow suppression. They must not be currently
      receiving prophylactic therapy for an opportunistic infection and must not have
      had an opportunistic infection within the past 6 months

      - NOTE: For patients who have received chemotherapy in the past 6 months, a CD4
      count < 250 cells/mcL during chemotherapy is permitted as long as viral loads
      were undetectable during this same chemotherapy. They must have an undetectable
      viral load and a CD4 count >= 250 cells/mcL within 7 days of
      registration/randomization

   - For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral
   load must be undetectable on suppressive therapy, if indicated

      - NOTE: Testing for HIV, hepatitis B or hepatitis C is not required unless
      clinically indicated

   - Patients with a history of hepatitis C virus (HCV) infection must have been treated
   and have undetectable viral load. For patients with HCV infection who are currently on
   treatment, they are eligible if they have an undetectable HCV viral load

   - Patients with known history or current symptoms of cardiac disease, or history of
   treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac
   function using the New York Heart Association Functional Classification. To be
   eligible for this trial, patients should be class 2B or better

   - Patient must have a body weight of > 30 kg

   - Patient must have life expectancy of >= 12 weeks

   - Patient must have creatinine clearance > 15 ml/min as by Crockroft-Gault formula or
   24-hour creatinine clearance within 28 days prior to registration/randomization

      - NOTE: Patients will be assigned to cisplatin-ineligible and cisplatin-eligible
      cohorts based on their creatinine clearance, Eastern Cooperative Oncology Group
      (ECOG) performance status, and grade (if any) of peripheral neuropathy and/or
      hearing loss in keeping with SOC cisplatin contraindications. Patients that are
      cisplatin-eligible will be randomized to either Arm A or Arm B

         - Patients that meet any of the following criteria will be registered and
         assigned to the cisplatin-ineligible Arm C if they meet other eligibility
         criteria:

            - Creatinine clearance > 15 ml/min and =< 50 ml/min or hearing loss grade
            >= 3, or neuropathy >= 2, or ECOG PS 2

            - Patient must have an absolute neutrophil count (ANC) >= 1,000/mcL
            obtained =< 14 days prior to registration

            - Patient must have ECOG performance status 0-2

         - Patients that meet the following criteria will be randomized to the
         cisplatin-eligible Arm A or Arm B:

            - Patient must have creatinine clearance of > 50ml/min, PS ECOG 0-1,
            absence of hearing loss grade >= 3, and/or neuropathy >= 2

            - Patient must have an absolute neutrophil count (ANC) >= 1,500/mcL
            obtained =< 14 days prior to randomization

            - Patient must have left ventricular ejection fraction (LVEF) >= 50% by
            (either multigated acquisition scan [MUGA] or 2-D echocardiogram)
            obtained within obtained within 28 days prior to randomization

Exclusion Criteria:

   - Patients must not have any component of small cell/neuroendocrine carcinoma. Other
   variant histologic types are permitted provided the predominant (>= 50%) subtype is
   urothelial carcinoma

   - Patients must not be pregnant or breast-feeding due to the potential harm to an unborn
   fetus and possible risk for adverse events in nursing infants with the treatment
   regimens being used. All patients of childbearing potential must have a blood test or
   urine study within 14 days prior to registration to rule out pregnancy. A patient of
   childbearing potential is defined as any patient, regardless of sexual orientation or
   whether they have undergone tubal ligation, who meets the following criteria: 1) has
   achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral
   oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer
   therapy does not rule out childbearing potential) for at least 24 consecutive months
   (i.e., has had menses at any time in the preceding 24 consecutive months)

   - Patients of childbearing potential and sexually active patients must not expect to
   conceive or father children, either by using accepted and effective method(s) of
   contraception or by abstaining from sexual intercourse from the time of registration,
   while on study treatment and for at least 6 months after the last dose of protocol
   treatment

   - Patients must have no evidence of metastatic disease or clinically enlarged regional
   lymph nodes (>= 1.5 cm short axis) on imaging required within 28 days prior to
   registration (Non-regional findings >=1.5 cm short axis that in the opinion of the
   investigator are not concerning for involvement based on radiographic characteristics,
   chronicity, avidity on positron emission tomography (PET) or other imaging or other
   criteria can be eligible based on investigator discretion).

      - NOTE: Patients with elevated alkaline phosphatase, calcium or suspicious bone
      pain/tenderness can also undergo baseline bone scans to evaluate for bone
      metastasis at the discretion of local provider.

   - Patient must meet below criteria for prior/current malignancy history:

      - Non-urothelial cancer malignancy history:

         - Patient must not have another active (or within two years) second malignancy
         other than resected non-melanoma skin cancers, resected in situ breast,
         cervical or other in situ carcinoma, and either clinically insignificant per
         the investigator (e.g. =< Gleason 3+4) on active surveillance (or watchful
         waiting) or previously treated prostate cancer with no rising prostate
         specific antigen (PSA) and no plan to treat

            - NOTE: Patients with a prior or concurrent malignancy whose natural
            history or treatment does not have the potential to interfere with the
            safety or efficacy assessment of the investigational regimen are
            eligible for this trial. Patients in whom concomitant or prior
            bladder/urethra predominant (>= 50%) urothelial carcinoma have been
            surgically resected and demonstrated to be only non-invasive cancer (<
            cT1N0) are eligible regardless of time elapsed

         - Urothelial cancer malignancy history:

            - Patient may have a history of resectable urothelial cancer as long as
            patients meet one of the following:

            - T0, Ta or Tis at any time

            - T1-4a N0 and no evidence of disease (NED) for more than 2 years from
            the latest therapy [e.g., radical surgery, transurethral resection of
            bladder tumor (TURBT), radiation, chemotherapy (neoadjuvant or
            adjuvant, or with radiation)]. Prior immune checkpoint inhibitor is not
            allowed.

            - Patient with history of >= pT4b, N+, and/or M1 is not eligible.

            - NOTE: Patients in whom concomitant or prior bladder/urethra predominant
            (>= 50%) urothelial carcinoma have been surgically resected and
            demonstrated to be only Ta or carcinoma in situ (CIS) (< cT1 N0) are
            eligible regardless of time elapsed

   - Patient must not have any uncontrolled illness including, but not limited to, ongoing
   or active infection including tuberculosis (clinical evaluation that includes clinical
   history, physical examination and radiographic findings, and tuberculosis [TB] testing
   in line with local practice), symptomatic congestive heart failure (CHF), myocardial
   infarction (MI) in last three months, or unstable angina pectoris, significant
   uncontrolled cardiac arrhythmia, clinically relevant liver cirrhosis, interstitial
   lung disease, or psychiatric illness/social situations that would limit compliance
   with study requirements

   - Patient must not have received prior radiation therapy to >= 25% of the bone marrow
   for other diseases

   - Patient must not have received prior systemic anthracycline therapy

      - NOTE: Patients who have received prior intravesical chemotherapy at any time for
      non-muscle invasive urothelial carcinoma of the bladder are eligible

   - Patient must not have either history of or active autoimmune disease requiring
   immunosuppressive therapy within 2 years prior to registration/randomization or any
   history of inflammatory bowel disease (inflammatory bowel disease [IBD], colitis, or
   Crohn's disease), neuromuscular autoimmune condition, immune-related pneumonitis or
   interstitial lung disease. Patients with well-controlled hyper/hypothyroidism, celiac
   controlled by diet alone, diabetes mellitus type I, vitiligo, alopecia, psoriasis,
   eczema, lichen planus, or similar skin/mucosa condition are eligible

   - Patient must not be on or have used immunosuppressive medication within 14 days prior
   to the first dose of durvalumab. The following are exceptions to this criterion:

      - Intranasal, inhaled, intra-auricular, topical steroids, or local steroid
      injections (e.g. intra-articular injection

      - Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of
      prednisone or its equivalent at the time of enrollment

      - Steroids as premedications for hypersensitivity reactions (e.g. computed
      tomography [CT] scan premedication)

   - Patient must not have received live attenuated vaccine within 30 days prior to the
   first dose of durvalumab, while on protocol treatment and within 30 days after the
   last dose of durvalumab

   - Patient must not have had a major surgical procedure within 28 days prior to
   registration/randomization

      - NOTE: Cystoscopy/ureteroscopy, stent placement or nephrostomy tube is not
      considered major surgery

   - Patient must not have history of allogenic organ transplantation