Cyclophosphamide and/or Mycophenolate Mofetil With or Without Tacrolimus in Treating Patients Who Are Undergoing a Donor Bone Marrow or Peripheral Stem Cell Transplant for Hematologic Cancer

OBJECTIVES: * Determine a minimal (short-duration) post-transplant immunosuppression regimen comprising cyclophosphamide and/or mycophenolate mofetil with or without tacrolimus that results in ≤ 20% incidence of grade II or higher acute graft-versus-host disease (GVHD) in patients with hematologic malignancies undergoing nonmyeloablative allogeneic bone marrow or peripheral blood stem cell transplantation from an HLA-identical related donor. * Determine the post-transplant immunosuppression regimen that results in \< 10% incidence of nonengraftment, defined as \< 5% donor chimerism in peripheral blood at day 60, in these patients. * Determine the incidence and severity of acute GVHD in patients treated with these regimens. * Determine the frequency of mixed chimerism in patients treated with these regimens. OUTLINE: * Nonmyeloablative allogeneic bone marrow transplantation (BMT) or peripheral blood stem cell transplantation (PBSCT): Patients receive fludarabine IV on days -4 to -2 and undergo total-body irradiation on day -1. Patients undergo allogeneic BMT on day 0 or PBSCT on day 0 (and days 1 and 2, if needed). Patients receive filgrastim (G-CSF) beginning on day 5 and continuing until at least day 15 or until blood counts recover. * Sequentially increasing levels of post-transplant immunosuppression: Cohorts of patients are enrolled into 1 of the following regimens: * Regimen 1 (post-BMT immunosuppression): Patients receive cyclophosphamide IV on day 3 only. * Regimen 2 (post-BMT immunosuppression): Patients receive mycophenolate mofetil (MMF) once on day 3 and then twice daily on days 4-32. * Regimen 3 (post-BMT immunosuppression): Patients receive cyclophosphamide IV on days 3 and 4 and MMF twice daily on days 4-33. * Regimen 4 (post-PBSCT immunosuppression): Patients receive cyclophosphamide and MMF as in regimen 3. * Regimen 5 (post-PBSCT immunosuppression): Patients receive cyclophosphamide and MMF as in regimen 3 and tacrolimus twice daily on days 4-33. Cohorts of approximately 10-20 patients receive sequentially increasing levels of post-transplant immunosuppression until a minimal (short-duration) post-transplant immunosuppression regimen is identified. The minimal post-transplant immunosuppression regimen is defined as the regimen in which ≤ 3 of 10 or ≤ 6 of 20 patients develop grade II or higher acute graft-versus-host disease AND ≤ 2 of 10 or ≤ 4 of 20 patients fail to engraft 60 days post-transplantation. Once the minimal post-transplant immunosuppression regimen is identified, an additional 10 patients are treated with that regimen. Patients are followed for 60 days after transplantation. PROJECTED ACCRUAL: A total of 60 patients will be accrued for this study.