This phase II trial studies donor atorvastatin treatment for the prevention of severe acute graft-versus-host disease (GVHD) in patients undergoing myeloablative peripheral blood stem cell (PBSC) transplantation. Giving chemotherapy and total-body irradiation (TBI) before a donor PBSC transplant helps stop the growth of cancer cells. It may also prevent the patient's immune system reject the donor's stem cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving atorvastatin to the donor before transplant may prevent this from happening.