Carfilzomib and Stem Cell Transplant for Plasma Cell Myeloma

Background: \- Plasma cell myeloma is a type of cancer that affects the plasma cells in the bone marrow. It can be difficult to treat with chemotherapy. One possible treatment combines chemotherapy with a stem cell transplant. To make this treatment more effective, researchers want to give another drug along with the transplant. This drug, carfilzomib, is often used to help treat plasma cell myeloma. However, it is not usually given along with the transplant. Researchers want to see if it is safe and effective to combine the stem cell transplant with carfilzomib, and if it improves the results of the transplant. Objectives: \- To test the safety and effectiveness of carfilzomib given with stem cell transplant for plasma cell myeloma. Eligibility: \- Individuals between 18 and 75 years of age who are having a stem cell transplant to treat plasma cell myeloma. Design: * Participants will be screened with a physical exam and medical history. Blood and urine samples will be collected. Imaging studies and a bone marrow biopsy will also be performed. * Participants will have their own stem cells collected for the transplant. The transplant will be performed according to the standard of care. * All participants will receive carfilzomib on the first 2 days after transplant. The study doctors will determine the number of additional doses that they may have. * Treatment will be monitored with frequent blood tests and imaging studies.