Rituximab in Preventing Acute Graft-Versus-Host Disease in a Donor Stem Cell Transplant for Hematologic Cancer

Inclusion Criteria: * Diagnosis of acute myeloid leukemia (AML), acute lymphoblastic leukemia (ALL), chronic myelogenous leukemia (CML) in accelerated phase or blast crisis, chronic lymphocytic leukemia (CLL), Non-Hodgkin lymphoma (NHL), myelodysplastic syndromes (MDS) (intermediate-2 or high-risk disease by International Pelvic Pain Society \[IPPS\]) * Patients with AML, ALL, or MDS scheduled for myeloablative conditioning should have =\< 10% blasts in bone marrow or peripheral blood at the start of conditioning * Patients with AML, ALL, or CML scheduled for reduced intensity conditioning or non-myeloablative conditioning should be in complete morphologic remission at the start of conditioning (residual disease by flow cytometry or cytogenetics and/or incomplete recovery of neutrophil or platelet count are acceptable) * Patients with CLL or NHL scheduled for reduced intensity or non-myeloablative conditioning should have no evidence of bulky disease (\> 50% bone marrow involvement or masses \> 10 cm) at the start of conditioning * Fulfills all pulmonary, cardiac, renal, and hepatic criteria for standard-of-care matched unrelated donor (MUD) allogeneic HCT * Men and women of reproductive potential must agree to use an acceptable method of birth control during treatment and for twelve months after stem cell transplantation * Adequately matched unrelated donor available * Written informed consent; written informed consent of the unrelated donor is required to participate in th…