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 the optional studies

Exclusion Criteria:

* Patient or donor infected with human immunodeficiency virus (HIV)
* Patient or donor with history of hepatitis B or C and/or positive serology consistent with previous hepatitis B or C infection (patients and/or donor who received Hepatitis B vaccination are acceptable)
* Patient or donor with active hepatitis B or C and/or detectable viral ribonucleic acid (RNA)
* More than 20,000 circulating CD20+ cells/uL
* Treatment with rituximab for any reason in the 12 months preceding HCT
* Patient scheduled for cord blood transplantation
* Presence of active uncontrolled infection at start of conditioning
* Presence of active central nervous system (CNS) disease (history of adequately treated CNS disease is acceptable)
* Presence of uncontrolled psychiatric disorder
* Patient unable to give informed consent
* Unrelated donor products received from the Deutsche Knochenmarkspenderdatei (DKMS) Registry are not eligible for the optional study