 This phase III trial studies the side effects of giving reduced-intensity conditioning followed by donor peripheral blood stem cell transplant PBSCT and how well it works in treating patients with multiple myeloma MM. Giving low doses of chemotherapy, such as fludarabine phosphate and melphalan, and total-body irradiation TBI before a donor PBSCT helps stop the growth of cancer cells. It may also stop the patients immune system from rejecting the donors stem cells. The donated stem cells may replace the patients immune cells and help destroy any remaining cancer cells graft-versus-tumor effect. Sometimes the transplanted cells from a donor can also make an immune response against the bodys normal cells. Giving mycophenolate mofetil and cyclosporine after transplant may stop this from happening. 