Tacrolimus and Mycophenolate Mofetil With or Without Sirolimus in Preventing Acute Graft-Versus-Host Disease in Patients Who Are Undergoing Donor Stem Cell Transplant for Hematologic Cancer

PRIMARY OBJECTIVES: I. To determine which of 3 GVHD prophylaxis regimens results in reduction of acute grades II-IV GVHD to =\< 40%. SECONDARY OBJECTIVES: I. Reduce the incidence of non-relapse mortality from infections and GVHD before day 200 to =\< 15%. II. Reduce the utilization of high-dose corticosteroids compared to protocols 1463, 1641, and 1668. III. Compare survival and progression-free survival to that achieved under protocols 1463, 1641, and 1668. OUTLINE: CONDITIONING: All patients receive fludarabine phosphate intravenously (IV) over 30 minutes on days -4 to -2 and undergo total-body irradiation on day 0. TRANSPLANTATION: All patients undergo allogeneic peripheral blood stem cell transplantation on day 0. IMMUNOSUPPRESSION: Patients are randomized to 1 of 3 treatment arms. ARM I: Patients receive tacrolimus IV or orally (PO) every 12 hours on days -3 to 180 with taper beginning on day 100 in the absence of GVHD. Patients also receive MMF PO every 8 hours on days 0-29 and then every 12 hours on days 30-96 with taper beginning on day 40 in the absence of GVHD. ARM II: Patients receive tacrolimus IV or PO every 12 hours on days -3 to 150 with taper beginning on day 100 in the absence of GVHD. Patients also receive MMF PO every 8 hours on days 0-29 and then every 12 hours on days 30-180 with taper beginning on day 150 in the absence of GVHD. ARM III: Patients receive tacrolimus and MMF as in arm II. Patients also receive sirolimus PO once daily on days -3 to 80. After completion of study treatment, patients are followed up at 6 months and then every year thereafter.