RO4929097 After Autologous Stem Cell Transplant in Treating Patients With Multiple Myeloma

This phase II clinical trial is studying how well gamma-secretase/Notch signalling pathway inhibitor RO4929097 (RO4929097) after autologous stem cell transplant works in treating patients with multiple myeloma. Giving chemotherapy, such as melphalan, before autologous stem cell transplant stops the growth of cancer cells by stopping them from dividing or killing them. Before treatment, stem cells are collected from the patient's blood and stored. After chemotherapy, the stem cells are returned to the patient to replace the blood-forming cells that were destroyed by the chemotherapy. RO4929097 may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Giving RO4929097 after autologous stem cell transplant may kill more cancer cells.