Haplo Peripheral Blood Sct In GVHD Prevention

Inclusion Criteria: * Men or women ≥ 18 and ≤ 80 years old * Diagnosis of hematological malignancy: * Acute myeloid leukemia (AML) or acute lymphoblastic leukemia (ALL) in morphologic complete remission * Myelodysplastic syndrome (MDS), myeloproliferative disorders (MPN), or chronic myelomonocytic leukemic (CMML) with \< 5% blasts in blood or bone marrow * Chemosensitive Hodgkin lymphoma (HL) or Non-Hodgkin lymphoma (NHL) * Patients must be undergoing haploidentical allogeneic hematopoietic cell transplantation, defined as 1st or 2nd degree relative with at least 5/10 matching at HLA-A, -B, -C, DR, and DQ. * ECOG performance status ≤2 * Patients with adequate physical function as measured by: * Cardiac: Left ventricular ejection fraction at rest must be ≥ 40%, or shortening fraction \>25% * Hepatic: * Bilirubin ≤ 2.5 mg/dL, except for patients with Gilbert's syndrome or hemolysis * ALT, AST, and Alkaline Phosphatase \< 5 x ULN * Renal: Serum creatinine within normal range, or if serum creatinine is outside normal range, then renal function (measured or estimated creatinine clearance or GFR) ≥ 40mL/min/1.73m2 * Pulmonary: DLCO (corrected for hemoglobin), FEV1 and FVC ≥ 50% predicted * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Prior allogeneic hematopoietic stem cell transplantation. (Patients may have received a prior autologous hematopoietic stem cell transplant.) * Participants who …