Cryopreserved MMUD BM With PTCy for Hematologic Malignancies

Inclusion Criteria: * Provision of signed and dated informed consent form * Stated willingness to comply with all study procedures and availability for the duration of the study * Male or female, aged ≥ 18 and \< 71 years (Note: HIV-negative subjects with MDS must be aged \<50 at the time of signing the informed consent form) * Diagnosed with * Acute leukemias or T-lymphoblastic lymphoma (T-LBL) in 1st or subsequent CR * Acute lymphocytic leukemia (ALL) or T-LBL as defined by the following: * \< 5% blasts in the bone marrow * Normal maturation of all cellular components in the bone marrow * No currently active extramedullary disease (EMD) (e.g., central nervous system (CNS), soft tissue disease) * ANC ≥ 1,000/mm3 * Acute myeloid leukemia (AML) defined by the following: * \< 5% blasts in the bone marrow * No blasts with Auer rods * Normal maturation of all cellular components in the bone marrow * No currently active EMD (e.g., CNS, soft tissue disease) * ANC ≥ 1,000/mm3 * Acute biphenotypic leukemia (ABL)/Acute undifferentiated leukemia (AUL) defined by the following: * \< 5% blasts in the bone marrow * Normal maturation of all cellular components in the bone marrow * No currently active EMD (e.g., CNS, soft tissue disease) * ANC ≥ 1,000/mm3 * Myleodysplastic Syndromes (MDS), fulfilling the following criteria: * Subjects with de novo MDS who have or have previously had Intermediate-2 or High-risk disease as determined by the IPSS. Current Intermediate-2 or High- risk disease is not a requirement * Subjects must have \< 20% bone marrow blasts, assessed within 60 days of informed consent * Subjects may have received prior therapy for the treatment of MDS prior to enrollment * Performance status: Karnofsky ≥ 60% * Adequate organ function defined as: * Cardiac: LVEF at rest ≥ 35% (RIC cohort) or LVEF at rest ≥ 40% (FIC cohort), or LVFS ≥ 25% * Pulmonary: DLCO, FEV1, FVC ≥ 50% predicted by pulmonary function tests (PFTs). DLCO value may be corrected or uncorrected for hemoglobin * Hepatic: total bilirubin ≤ 2.5 mg/dL, and ALT, AST, and ALP \< 5 x ULN (unless ALT, AST, and/or ALP are disease related) * Renal: SCr within normal range for age (see table 5.1B). If SCr is outside normal range for age, CrCl \> 40 mL/min/1.73m2 must be obtained (measured by 24-hour (hr) urine specimen or nuclear glomerular filtration rate (GFR), or calculated GFR (by Cockcroft-Gault formula) * Subjects must have the ability to give informed consent according to applicable regulatory and local institutional requirements * Availability of deceased HLA MMUD cryopreserved product through Ossium cryobank * HLA MMUD defined as 4-7/8 HLA-allele matching at MHC class (A, B, or C) or MHC class II (DRB1) * Additional MHC class II HLA (DP and DQ) typing will be collected, but not incorporated in donor selection Exclusion Criteria: * Pediatric patients (17 years or younger) * Suitable HLA-matched related or 8/8 allele matched (HLA-A, -B, -C, -DRB1) unrelated donor excluding Ossium product * Autologous HCT \< 3 months prior to the time of signing the informed consent form * Pregnancy or lactation * Treatment with an investigational drug or other interventional GVHD clinical trials * Current uncontrolled bacterial, viral or fungal infection (currently taking medication with evidence of progression of clinical symptoms or radiologic findings) * Prior allogeneic HCT * Primary myelofibrosis or myelofibrosis secondary to essential thrombocythemia or polycythemia vera * Subjects with MDS may not receive RIC and must be \< 50 years of age at the time of signing the informed consent form * Any condition(s) or diagnosis, both physical or psychological, or physical exam finding that in the investigator's opinion precludes participation