Busulfan, Cyclophosphamide, & Antithymocyte Globulin Followed by Stem Cell Transplant in Treating Hematologic Cancer

Inclusion Criteria: * Pathologically confirmed diagnosis of 1 of the following: * Acute myeloid leukemia * Acute lymphocytic leukemia * Chronic myelogenous leukemia beyond first chronic phase (i.e., 2nd chronic phase, accelerated phase, or blast crisis) * Multiple myeloma * Myelodysplastic syndromes * Malignant lymphoma * Myelofibrosis * Requirement for myeloablative conditioning regimen confirmed by attending physician * Available donor must meet the following criteria: * HLA phenotypically identical unrelated donor by low, intermediate, or high resolution for HLA class I antigens, and by high resolution for HLA class II antigens * Matched at the A, B, and DRβ1 loci * Single HLA-A or HLA-B antigen mismatch allowed * Meets all National Marrow Donor Program or foreign registry criteria for allogeneic bone marrow/stem cell donors * Peripheral blood stem cells are the preferred product on this study but bone marrow is allowed * Karnofsky performance status 70-100% * DLCO ≥ 50% predicted * LVEF ≥ 45% * Serum creatinine ≤ 1.5 mg/dL or creatinine clearance ≥ 65 mL/min * Serum total bilirubin ≤ 2.0 mg/dL * Fertile patients must use effective contraception Exclusion Criteria: * No active uncontrolled infection * Not pregnant or nursing/negative pregnancy test * No HIV infection * No chronic active hepatitis B or C or evidence of cirrhosis on liver biopsy