OUTLINE: Conditioning: Patients undergo low dose total body irradiation followed by infusion of allogeneic peripheral blood stem cells (PBSC) on day 0. Donor lymphocyte infusions: Nonmobilized donor lymphocytes are harvested from the same HLA identical related donor on day 95 after PBSC transplantation. Eligible patients with mixed chimerism and no graft versus host disease (GVHD) receive the first donor lymphocyte infusion (DLI) on the same day that donor lymphocytes are collected. Patients who continue to have mixed chimerism and no GVHD receive the second DLI at a higher dose level on day 65 after the first DLI. Patients are followed weekly until day 90, and then monthly thereafter.