Autologous transplant is now considered a standard treatment for many patients with multiple myeloma. An autologous transplant is a procedure in which stem cells are removed from a patient and then given back to the patient following intensive treatment. Doctors remove healthy stem cells from a patient's circulating blood system and store them before the patient receives high-dose chemotherapy. The stem cells are then returned to the patient, where they can produce new blood cells to replace cells destroyed by the treatment. The drug usually used before transplant is melphalan alone in 1 or 2 high doses. In past studies conducted at UAMS, researchers have shown that a chemotherapy treatment regimen called "VTD" is effective in patients with multiple myeloma who have failed previous treatments. VTD is a combination of drugs consisting of VelcadeTM (also known as bortezomib), Thalidomide, and Dexamethasone. In this study, researchers want to find out if using the VTD regimen, along with higher doses melphalan, in subjects who have relapsed or progressed after previous transplant(s) can be given safely to subjects who have failed previous transplant(s).