OUTLINE: This is a multicenter study. Patients undergo leukapheresis to collect white blood cells which are incubated with donor bone marrow cells in the presence of CTLA4-Ig for 36 hours. Patients undergo total body irradiation on days -7, -6, -5, and -4 and receive cyclophosphamide IV on days -3 and -2. Patients with acute lymphocytic leukemia, prior lymphoid blast crisis chronic myelogenous leukemia, high grade non-Hodgkin's leukemia (NHL), intermediate grade NHL with prior marrow or extramedullary disease, or prior CNS leukemia receive 2 doses of methotrexate intrathecally prior to bone marrow transplantation, and 4-6 doses following. Patients receive bone marrow transplantation on day 0; methotrexate IV on days 1, 3, 6, and 11; and cyclosporine IV on days -1 to 50. Patients are followed weekly for 1 month, monthly for 2 years, and then annually thereafter.