OBJECTIVES: I. Determine the incidence and severity of acute graft versus host disease after transplantation of HLA haploidentical bone marrow preincubated with alloantigen and CTLA4-Ig ex vivo in patients with hematologic malignancies. II. Determine the engraftment rate with this treatment regimen in these patients. III. Determine the safety of this treatment regimen in these patients. IV. Determine the incidence of infection and relapse after this treatment regimen in these patients. V. Determine whether host specific tolerance develops in these patients after receiving this treatment regimen.