Stratum 1 Recipient Inclusion Criteria:

   1. Age ≥ 18 years and < 66 years (chemotherapy-based conditioning) or < 61 years (total
   body irradiation [TBI]-based conditioning) at the time of signing informed consent

   2. Patient or legally authorized representative has the ability to provide informed
   consent according to the applicable regulatory and institutional requirements.

   3. Stated willingness to comply with all study procedures and availability for the
   duration of the study.

   4. Planned MAC regimen as defined per study protocol

   5. Available partially HLA-MMUD (4/8-7/8 at HLA-A, -B, -C, and -DRB1 is required) with
   age ≥ 18 and ≤ 40 years (≤ 35 preferred).

   6. Product planned for infusion is MMUD T-cell replete PBSC allograft

   7. HCT-CI < 5. The presence of prior malignancy will not be used to calculate HCT-CI for
   this trial to allow for the inclusion of patients with secondary or therapy-related
   AML or MDS.

   8. One of the following diagnoses:

      1. Acute myeloid leukemia (AML), acute lymphoblastic leukemia (ALL), or other acute
      leukemia in 1st remission or beyond with ≤ 5% marrow blasts and no circulating
      blasts or evidence of extra-medullary disease. Documentation of bone marrow
      assessment will be accepted within 45 days prior to the anticipated start of
      conditioning.

      2. Patients with MDS with no circulating blasts and with < 10% blasts in the bone
      marrow (higher blast percentage allowed in MDS due to lack of differences in
      outcomes with < 5% or 5-10% blasts in MDS). Documentation of bone marrow
      assessment will be accepted within 45 days prior to the anticipated start of
      conditioning.

   9. Cardiac function: Left ventricular ejection fraction ≥ 45% based on most recent
   echocardiogram or multi-gated acquisition scan (MUGA) results.

10. Estimated creatinine clearance ≥ 45mL/min calculated by equation.

11. Pulmonary function: diffusing capacity of the lungs for carbon monoxide (DLCO)
   corrected for hemoglobin > 50% and forced expiratory volume in first second (FEV1)
   predicted > 50% based on most recent pulmonary function test (PFT) results

12. Liver function acceptable per local institutional guidelines

13. KPS of ≥ 70%

Stratum 2 Recipient Inclusion Criteria:

   1. Age ≥18 years at the time of signing informed consent

   2. Patient or legally authorized representative has the ability to provide informed
   consent according to the applicable regulatory and local institutional requirements.

   3. Stated willingness to comply with all study procedures and availability for the
   duration of the study.

   4. Planned NMA/RIC regimen per study protocol

   5. Available partially HLA-MMUD (4/8-7/8 at HLA-A, -B, -C, and -DRB1 is required) with
   age ≥ 18 and ≤ 40 years (≤ 35 preferred).

   6. Product planned for infusion is MMUD T-cell replete PBSC allograft

   7. One of the following diagnoses:

      1. Patients with acute leukemia or chronic myeloid leukemia (CML) with no
      circulating blasts, no evidence of extramedullary disease, and with < 5% blasts
      in the bone marrow.

      Documentation of bone marrow assessment will be accepted within 45 days prior to
      the anticipated start of conditioning.

      2. Patients with MDS with no circulating blasts and with < 10% blasts in the bone
      marrow (higher blast percentage allowed in MDS due to lack of differences in
      outcomes with < 5% or 5-10% blasts in MDS.) Documentation of bone marrow
      assessment will be accepted within 45 days prior to the anticipated start of
      conditioning.

      3. Patients with chronic lymphocytic leukemia (CLL) or other leukemias (including
      prolymphocytic leukemia) with chemosensitive disease at time of transplantation

      4. Higher risk CMML according to CMML-specific prognostic scoring system or high
      risk MDS/MPN not otherwise specified are eligible, provided there is no evidence
      of high-grade bone marrow fibrosis or massive splenomegaly at the time of
      enrollment.

      5. Patients with lymphoma with chemosensitive disease at the time of transplantation

   8. Cardiac function: Left ventricular ejection fraction ≥ 40% based on most recent
   echocardiogram or MUGA results with no clinical evidence of heart failure

   9. Estimated creatinine clearance ≥ 45mL/min calculated by equation

10. Pulmonary function: DLCO corrected for hemoglobin > 50% and FEV1 predicted >50% based
   on most recent PFT results

11. Liver function acceptable per local institutional guidelines

12. KPS of ≥ 60%

Stratum 3 Recipient Inclusion Criteria:

   1. Age ≥18 years at the time of signing informed consent

   2. Patient or legally authorized representative has the ability to provide informed
   consent according to the applicable regulatory and local institutional requirements.

   3. Stated willingness to comply with all study procedures and availability for the
   duration of the study.

   4. Planned NMA/RIC regimen per study protocol

   5. Available partially HLA-MMUD (4/8-7/8 at HLA-A, -B, -C, and -DRB1 is required) with
   age ≥ 18 and ≤ 40 years (≤ 35 preferred).

   6. Product planned for infusion is MMUD T-cell replete PBSC allograft

   7. Diagnosis of primary myelofibrosis with risk features making them eligible for HCT.
   Myelofibrosis secondary to essential thrombocythemia, polycythemia vera, or MDS with
   grade 4 fibrosis are also eligible. Patients with a myelofibrosis diagnosis require
   sponsor approval before enrolling.

   8. Cardiac function: Left ventricular ejection fraction ≥ 40% based on most recent
   echocardiogram or MUGA results with no clinical evidence of heart failure

   9. Estimated creatinine clearance ≥ 45 mL/min calculated by equation

10. Pulmonary function: DLCO corrected for hemoglobin > 50% and FEV1 predicted >50% based
   on most recent PFT results

11. Liver function acceptable per local institutional guidelines

12. KPS of ≥ 60%

Donor Inclusion Criteria (note: donors are not research subjects):

   1. Must be unrelated to the subject and high-resolution HLA-matched at 4/8, 5/8, 6/8, or
   7/8 (HLA-A, -B, -C, and -DRB1.

   2. Donor must be typed at high-resolution for a minimum of HLA-A, -B, -C, -DQB1, and
   -DPB1.

   3. Age ≥ 18 years and ≤ 40 years at the time of signing informed consent for PBSC
   donation. Note: donors are preferred to be ≤ 35.

   4. Meet the donor registries' medical suitability requirements for PBSC donation.

   5. Must undergo eligibility screening according to current Food and Drug Administration
   (FDA) requirements. Donors who do not meet one or more of the donor screening
   requirements may donate under urgent medical need.

   6. Must agree to donate PBSC.

   7. Must have the ability to give informed consent according to standard (non-study)
   informed consent according to applicable donor regulatory requirements.

Recipient Exclusion Criteria (Strata 1, 2, and 3):

   1. Suitable HLA-matched related or 8/8 high-resolution matched unrelated donor available

   2. Subject unwilling or unable to give informed consent, or unable to comply with the
   protocol including required follow-up and testing

   3. Subjects with a prior allogeneic transplant

   4. Subjects with an autologous transplant within the past 3 months

   5. Females who are breast-feeding or pregnant

   6. Uncontrolled bacterial, viral, or fungal infection at the time of the transplant
   preparative regimen

   7. Concurrent enrollment on a preventative GvHD and/or infectious disease prevention
   clinical trial.

   8. Subjects who undergo desensitization to reduce anti-donor HLA antibody levels prior to
   transplant.

   9. Patients who are HIV+ with persistently positive viral load. HIV-infected patients on
   effective anti-retroviral therapy (ART) with undetectable viral load within 6 months
   are eligible for this trial. Patients with well controlled HIV are eligible provided
   resistance panels are negative, the patient is compliant with ART, and their disease
   remains well controlled.

Donor Exclusion Criteria:

   1. Donor unwilling or unable to donate.

   2. Recipient positive for HLA antibodies against a mismatched HLA in the selected donor
   determined by the presence of donor specific HLA antibodies (DSA) to any mismatched
   HLA allele/antigen at any of the following loci (HLA-A, -B, -C, -DRB1, DRB3, DRB4,
   DRB5, -DQA1, - DQB1, -DPA1, -DPB1) with median fluorescence intensity (MFI) >3000 by
   microarray-based single antigen bead testing. In patients receiving red blood cell or
   platelet transfusions, DSA evaluation must be performed or repeated post-transfusion
   and prior to donor mobilization and initiation of recipient preparative regimen.