DISEASE CHARACTERISTICS: Histologically proven hematologic malignancy for which there is no standard curative therapy, including, but not limited to: Low grade non-Hodgkin's lymphoma (NHL) Mantle cell lymphoma Chronic lymphocytic leukemia (stage II-IV) Myelodysplastic syndrome, including: Refractory anemia (RA) with ringed sideroblasts RA with excess blasts (RAEB) RAEB in transformation Chronic myelomonocytic leukemia Multiple myeloma OR Histologically proven hematologic malignancy that has failed 1 prior therapy OR is at high risk for relapse, including, but not limited to: Intermediate grade NHL High grade NHL Hodgkin's disease Acute lymphoblastic lymphoma Acute myelogenous leukemia OR Histologically proven chronic myelogenous leukemia in chronic or accelerated phase, with the following risk factors that preclude eligibility for standard allogeneic peripheral blood stem cell transplantation: Older age Poor performance status Healthy, partially related HLA 5/6 or 6/6 serologic match donor available A new classification scheme for adult non-Hodgkin's lymphoma has been adopted by PDQ. The terminology of "indolent" or "aggressive" lymphoma will replace the former terminology of "low", "intermediate", or "high" grade lymphoma. However, this protocol uses the former terminology.