Study to Characterize Mismatched to Fully HLA-Matched Ossium HPC, Marrow and Living Donor Transplantation in Patients With Hematologic Malignancies

Inclusion Criteria: 1. Patient has the ability to provide informed consent according to the applicable regulatory and local institutional requirements. 2. Male or female, aged ≥12 and ≤65 years for patients receiving MAC aged ≥12 and ≤75 years for patients receiving RIC. Patients between 75 and 80 years on RIC regimen can be enrolled with prior sponsor approval 3. Patient must require first allogeneic HCT per the discretion of the treating physician 4. BMI \<=50 (BMI of 45.1 to 50 maybe allowed after sponsor approval) 5. For treatment from Ossium product only- no suitable donor available after 3 weeks of search 6. Patient must be high-resolution: 1. HLA partially or fully matched (4-8/8 allele matched at HLA-A, -B, -C, DRB1) to an available Ossium HPC, Marrow product for experimental arm 2. HLA fully matched (8/8 allele matched at HLA-A, -B, -C, DRB1) to an unrelated available PBSC donor for observational standard of care arm 3. HLA partially matched (4-7/8 allele matched at HLA-A, -B, -C, DRB1) to an available PBSC donor for observational standard of care arm 4. HLA haploidentical matched (4/8 allele matched at HLA-A, -B, -C, DRB1) to available PBSC donor for observational standard of care arm 5. HLA partially matched (4-8/8 allele matched at HLA-A, -B, -C, DRB1) to an available living bone marrow donor for optional observational standard of care arm 7. Stated willingness to comply with all study procedures and availability for the duration of the study 8. Patient with malignant hematologic disease including: 1. Diagnosed with acute leukemia \[acute lymphoblastic leukemia (ALL), acute myeloid leukemia (AML), acute biophenotypic leukemia (ABL), or acute undifferentiated leukemia (AUL)\], , in the first remission or beyond with ≤5% marrow blasts and no circulating blasts or extra-medullary disease documented by bone marrow assessment within 42 days prior to anticipated start of conditioning or 2. MDS without Grade 3 fibrosis (Patients with Grade 1 and Grade 2 fibrosis can be enrolled with prior sponsor approval) 3. Chronic Lymphocytic Leukemia (CLL) eligible for allogeneic transplant or 4. Chronic Myeloid leukemia (CML) eligible for allogeneic transplant 5. Chemosensitive lymphomas in the first remission or beyond documented by PET/CT imaging and bone marrow assessment within 42 days prior to anticipated start of conditioning 6. Other rare hematological malignancy indications eligible for allogenic transplant will require prior sponsor review and approval 7. Absence of active CNS disease due to underlying hematological disease 9. Karnofsky performance status score ≥70% (MAC) or ≥60% (RIC) 10. HCT comorbidity index (HCT-CI) ≤5 11. Adequate organ function defined as: 1. Cardiac: LVEF at rest ≥40% (RIC) or LVEF at rest ≥45% (MAC) 2. Pulmonary: DLCO, FEV1, FVC ≥50% predicted by pulmonary function tests (PFTs). DLCO value may be corrected (dinakara correction) for hemoglobin. 3. Hepatic: total bilirubin ≤2.0 mg/dL (except Gilbert syndrome ), and ALT, AST, and ALP \<3 x upper limit normal (ULN), unless ALT, AST, and/or ALP are disease related 4. Renal: CrCl\> 45 mL/min/1.73m2 must be obtained (measured by 24-hour urine specimen or nuclear glomerular filtration rate (GFR), or calculated GFR (by Cockcroft-Gault formula)) or Cystatin-C test. Exclusion Criteria: 1. Autologous transplant within 6 months 2. Prior allogeneic HCT 3. Myeloproliferative disorders or MDS with grade 3 and higher fibrosis are excluded 4. HTLV-ATLL positive patients are excluded 5. Currently Pregnant or Currently lactating parent 6. Participation with an investigational trial within 3 months of planned transplant (Note: participation in survey studies or standard of care studies maybe allowed after sponsors approval or are part of long term follow up for an interventional trial) 7. Recipient of allogeneic CART-T therapy 8. Recipient of checkpoint inhibitor in last 3 months 9. Current uncontrolled bacterial, viral or fungal infection defined as currently taking medication with evidence of progression of clinical symptoms or radiologic findings 10. Any condition(s) or diagnosis, both physical or psychological, or physical exam finding that in the investigator's opinion precludes participation 11. Presence of donor-specific antibodies. Recipient has positive anti-donor HLA antibodies against a mismatched HLA in the selected donor determined by either: 1. positive crossmatch test of any titer (by complement-dependent cytotoxicity or flow cytometric testing) or 2. presence of donor specific HLA antibodies (DSA) to any mismatched HAS allele/antigen at any of the following loci (HLA-A, -B, -C, -DRB1, -DPA1, -DPB1) with median fluoresce intensity (MFI) \>3000 by Luminex single antigen bead based solid phase immunoassay tested prior to SSA request and repeated if transplant is \>30 days from prior HLA antibody testing or if patient receives additional blood products/transfusion prior to transplant 3. Patients with donor specific HLA antibodies (DSA) to donor that is reduced post treatment of de-sensitization for DSA