DISEASE CHARACTERISTICS: Histologically proven advanced hematologic malignancy unsuitable for standard allogeneic bone marrow transplantation One of the following types: Refractory or relapsed acute myelogenous or lymphocytic leukemia Over 55 years Chronic myelogenous leukemia and failed interferon treatment Over 55 years Lymphoma, chronic lymphocytic leukemia, Hodgkin's disease, or multiple myeloma: Refractory OR More than 2 relapses OR Relapse after autologous peripheral blood stem cell transplantation Myelodysplastic syndrome other than refractory anemia Severe aplastic anemia Under 55 years and either organ dysfunction or not eligible for standard allogeneic bone marrow transplant due to one or more of the following: Chronic hepatitis LVEF less than 50% Karnofsky less than 70% Unrelated matched donor available