RATIONALE: A peripheral stem cell transplant or an umbilical cord blood transplant from a donor may be able to replace blood-forming cells that were destroyed by chemotherapy or radiation therapy. Giving an infusion of the donor's white blood cells (donor lymphocyte infusion) after the transplant may help destroy any remaining cancer cells (graft-versus-tumor effect). Sometimes the transplanted cells can make an immune response against the body's normal cells. Methotrexate, cyclosporine, tacrolimus, or methylprednisolone may stop this from happening.