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

The purpose of this study is to see if a condensed version of the chemotherapy regimen busulfan, melphalan, fludarabine (bu/mel/flu) and the drug antithymocyte globulin (ATG-also referred to as rATG or thymoglobulin) can have the same or fewer number of severe side effects in people with various blood cancers 30 days after they receive an allogeneic hematopoietic 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 \