Sirolimus, Tacrolimus, and Antithymocyte Globulin in Preventing Graft-Versus-Host Disease in Patients Undergoing a Donor Stem Cell Transplant For Hematological Cancer

DISEASE CHARACTERISTICS: * Diagnosis of hematological malignancy including any of the following: * Non-Hodgkin lymphoma (NHL) in any complete remission (CR) or partial response (PR) * Hodgkin lymphoma in any CR or PR * Acute myeloid leukemia (AML) or acute lymphoblastic leukemia (ALL) in any CR * Bone marrow blasts \< 20% within 4 weeks of transplant and peripheral blood absolute blast count \< 500/µL on the day of initiation of conditioning for patients with non-CR AML or ALL * Myelodysplastic syndromes (MDS) treated or untreated * Chronic myelogenous leukemia (CML) in chronic or accelerated phase * Multiple myeloma in any CR or PR * Chronic lymphocytic leukemia in CR or PR 2 or greater * Myelofibrosis and other myeloproliferative disorders * Bone marrow blasts \< 20% within 4 weeks of transplant and peripheral blood absolute blast count \< 500/µL on the day of initiation * High-risk disease defined as AML or ALL \> CR1, accelerated phase CML, recurrent aggressive lymphoma, or active lymphoproliferative disease at transplant * Low-risk disease defined as AML or ALL in CR1, chronic phase CML, or low-grade lymphoproliferative disorder with controlled disease at transplant * Must be planning to receive 1 of the following conditioning regimens at City of Hope: * Fludarabine phosphate and melphalan for patients with hematological malignancies and contraindications for conventional myeloablative regimens due to age, co-morbidity, or previous transpla…