High Dose Cyclophosphamide, Tacrolimus, and Mycophenolate Mofetil in Preventing Graft Versus Host Disease in Patients With Hematological Malignancies Undergoing Myeloablative or Reduced Intensity Donor Stem Cell Transplant

Inclusion Criteria: * Patients with acute leukemia or chronic myelogenous leukemia with no circulating blasts and with less than 10% blasts in the bone marrow * Patients with myelodysplastic syndrome (MDS) with intermediate-2 or high risk per International Prognostic Scoring System (IPSS) (or intermediate, high, very high risk by Revised International Prognostic Scoring System \[IPSS-R\]) or myeloproliferative neoplasm; primary or secondary if high-risk features or refractory disease * Patients with chronic lymphocytic leukemia/small lymphocytic lymphoma, follicular, marginal zone, diffuse large B-cell, Hodgkin lymphoma, or mantle cell lymphoma with chemosensitive disease at time of transplantation; all types of lymphoma are eligible * High risk, or refractory and relapsed multiple myeloma * No available human leukocyte antigen (HLA)-matched related donor * Available matched unrelated donor * Ejection fraction at rest \>= 50% * Karnofsky performance status (KPS) \>= 70 * Measured creatinine clearance more than 60 mL/min. The updated Schwartz formula should be used for pediatric patients (\>=5 to 12 years old) * Carbon monoxide diffusing capability test (DLCO) \>= 50% (adjusted for hemoglobin) and forced expiratory volume in 1 second (FEV1) \>= 50% * Total bilirubin \< 1.5 x the upper limit of normal; patients who have been diagnosed with Gilbert's disease are allowed to exceed the defined bilirubin value of 1.5 x the upper limit of normal * Alanine aminotransferase (ALT)/asp…