Autologous Peripheral Blood Stem Cell Transplant Followed by Donor Bone Marrow Transplant in Treating Patients With High-Risk Hodgkin Lymphoma, Non-Hodgkin Lymphoma, Multiple Myeloma, or Chronic Lymphocytic Leukemia

This phase II trial studies autologous peripheral blood stem cell transplant followed by donor bone marrow transplant in treating patients with high-risk Hodgkin lymphoma, non-Hodgkin lymphoma, multiple myeloma, or chronic lymphocytic leukemia. Autologous stem cell transplantation uses the patient's stem cells and does not cause graft versus host disease (GVHD) and has a very low risk of death, while minimizing the number of cancer cells. Peripheral blood stem cell (PBSC) transplant uses stem cells from the patient or a donor and may be able to replace immune cells that were destroyed by chemotherapy. These donated stem cells may help destroy cancer cells. Bone marrow transplant known as a nonmyeloablative transplant uses stem cells from a haploidentical family donor. Autologous peripheral blood stem cell transplant followed by donor bone marrow transplant may work better in treating patients with high-risk Hodgkin lymphoma, non-Hodgkin lymphoma, multiple myeloma, or chronic lymphocytic leukemia.