Fludarabine Phosphate and Total-Body Radiation Followed by Donor Peripheral Blood Stem Cell Transplant and Immunosuppression in Treating Patients With Hematologic Malignancies

Inclusion Criteria: * Patients with non-Hodgkin lymphoma (NHL), chronic lymphocytic leukemia (CLL) or multiple myeloma who are not eligible for a curative autologous transplantation or who have received a prior autologous transplantation; patients with NHL or CLL must have failed prior therapy with an alkylating agent and/or fludarabine, or be at high risk of relapse; patients with multiple myeloma must have stage II or III disease and received prior chemotherapy * Patients \< 50 years of age with NHL, Hodgkin's disease (HD), CLL or multiple myeloma at high risk of regimen related toxicity through prior autologous transplant or through pre-existing medical conditions * Patients \< 75 years of age with other malignant diseases treatable by allogeneic bone marrow transplant (BMT) whom through pre-existing chronic disease affecting kidneys, liver, lungs, and heart are considered to be at high risk for regimen related toxicity using standard high dose regimens; the following diseases are the likely candidates * Myelodysplastic syndromes * Myeloproliferative syndromes * Acute Leukemia with \< 10% blasts * Amyloidosis * Hodgkin's disease * The Fred Hutchinson Cancer Research Center (FHCRC) Patient Care Conference (PCC) may approve patients with other malignancies or patients declining standard allografts for transplant following presentation and approval; centers outside the FHCRC that have a PCC or equivalent should obtain their Institutional approval; if there is not …