Giving Chemotherapy for a Shortened Amount of Time Before a Stem Cell Transplantation

Inclusion Criteria: * Patients aged ≥ 18 years old. * Patients with any of the following hematologic malignancies for which allo-HCT is indicated, including: * Acute myeloid leukemia (AML) with intermediate or high-risk features in CR1. * Relapsed AML in ≥ CR2. * Acute leukemias of ambiguous lineage in ≥ CR1. * Acute lymphoid leukemia (ALL) in CR1 with clinical, flow cytometric, or molecular features indicating a high risk for relapse, or ALL in ≥ CR2. * CML meeting one of the following criteria: * Failed response to or intolerant to BCR-ABL tyrosine kinase inhibitors (TKIs). * CML with BCR-ABL mutation consistent with poor response to TKIs (e.g., T315I mutation) * CML in accelerated phase or blast crisis with \<10% blasts after therapy, or in second chronic phase. * Myelodysplastic syndromes (MDS), myeloproliferative neoplasms (MPN), or MDS/MPN overlap syndromes with least one of the following: * Revised International Prognostic Scoring System risk score of intermediate or higher at the time of transplant evaluation. * Life-threatening cytopenias. * Karyotype or genomic changes that indicate high risk for progression to acute myelogenous leukemia, including abnormalities of chromosome 7 or 3, mutations of TP53, or complex or monosomal karyotype. * Therapy related disease or disease evolving from other malignant processes. * Chronic myelomonocytic leukemia (CMML-1 or CMML-2). * Severe aplastic anemia. * Relapsed Hodgkin lymphoma meeting both of the following criteria: * Responding to therapy prior to enrollment. * Relapse after autologous HCT or are ineligible for autologous HCT. * Relapsed non-Hodgkin lymphoma meeting both of the following criteria: * Responding to therapy prior to enrollment. * Relapse after prior autologous HCT or are ineligible for autologous HCT. * High-risk multiple myeloma following autologous HCT or relapsed multiple myeloma following autologous HCT with chemosensitive disease. * Adequate organ function is required, defined as follows: * Serum bilirubin ≤ 2 mg/dL, unless benign congenital hyperbilirubinemia. Patients with hyperbilirubinemia related to paroxysmal nocturnal hemoglobinuria or other hemolytic disorders are eligible with PI approval. * AST, ALT, and alkaline phosphatase \< 3 times the upper limit of normal unless thought to be disease-related. * Creatinine clearance ≥ 50 ml/min (calculated by Cockcroft Gault) * LVEF ≥ 45% by MUGA or resting echocardiogram. * Pulmonary function (FEV1 and corrected DLCO) ≥ 50% predicted. * Adequate performance status of ECOG ≤ 2. * Each patient must be willing to participate as a research subject and must sign an informed consent form. Exclusion Criteria: * Patients with active extramedullary disease. * Patients with active central nervous system malignancy. * Active and/or uncontrolled infection at the time of allo-HCT. * Patients who have undergone previous allo-HCT. * Patients who have undergone previous autologous HCT within the last 6 months, with the exclusion of high-risk multiple myeloma patients. * Patient seropositivity for HIV I/II and/or HTLV I/II. * Females who are pregnant or breastfeeding. * Patients unwilling to use contraception during the study period. * Patient or guardian unable to give informed consent or unable to comply with the treatment protocol. Donor Inclusion and Exclusion Criteria: * Must be a 10/10 HLA genotypically matched related or unrelated donor at A, B, C, DRB1, and DQB1 loci, as tested by DNA analysis. * Able to provide informed consent for the donation process per institutional standards. * Meet standard criteria for donor collection as defined by the National Marrow Donor Program Guidelines.