Sirolimus, Tacrolimus, Thymoglobulin and Rituximab as Graft-versus-Host-Disease Prophylaxis in Patients Undergoing Haploidentical and HLA Partially Matched Donor Hematopoietic Cell Transplantation

DISEASE CHARACTERISTICS: * Diagnosis of a hematological malignancy, including: * Non-Hodgkin lymphoma * Hodgkin lymphoma * Acute myeloid leukemia or acute lymphoblastic leukemia * Myelodysplastic syndrome (treated or untreated) * Chronic myelogenous leukemia * Multiple myeloma * Chronic lymphocytic leukemia * Myelofibrosis and other myeloproliferative disorders * No suitable related HLA-matched or unrelated HLA-matched (8/8 or 7/8 matched) donor * Available suitable haploidentical or partial-matched unrelated donor (high-resolution molecular HLA typing is mandatory for HLA Class I and II) * No more than 4/8 HLA allele or antigen mismatch for a haploidentical-related first-degree family member donor * Only 6/8 or 5/8 allele or antigen match for an unrelated donor * Scheduled to undergo peripheral blood stem cell transplantation * Not receiving bone marrow or ex vivo engineered or processed graft (e.g., CD34+ enrichment, T-cell depletion) * No documented uncontrolled CNS disease PATIENT CHARACTERISTICS: * Karnofsky performance status (PS) 70-100% * ECOG PS 0-2 * Serum bilirubin \< 3 times upper limit of normal (ULN) * ALT and AST \< 3 times ULN * Creatinine clearance \> 60 mL/min * Ejection fraction \> 50% * Forced vital capacity, FEV\_1, or DLCO \> 50% predicted * Negative pregnancy test * Able to cooperate with oral medication intake * Patients with coronary heart disease (recent myocardial infarctions, angina, cardiac stent, or bypass surgery in t…