This pilot clinical trial studies low-dose total body irradiation and donor peripheral blood stem cell transplant followed by donor lymphocyte infusion in treatment patients with non-Hodgkin lymphoma, chronic lymphocytic leukemia, or multiple myeloma. Giving total-body irradiation before a donor peripheral blood stem cell transplant helps stop the growth of cells in the bone marrow, including normal blood-forming cells (stem cells) and cancer cells. When 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. Once the donated stem cells begin working, the patient's immune system may see the remaining cancer cells as not belonging in the patient's body and destroy them. Giving an infusion of the donor's white blood cells (donor lymphocyte infusion) may boost this effect.