Patients will undergo a steady state leukapheresis (Xcellerate Leukapheresis) to obtain peripheral blood mononuclear cells that will be used to produce Xcellerated T Cells. During the Xcellerate Process, T cells will be activated and expanded ex vivo by co-stimulation with anti-CD3 and anti-CD28 monoclonal antibodies covalently attached to super-paramagnetic microbeads. While the Xcellerated T Cells are being produced at Xcyte Therapies, patients will be treated with a standard mobilization regimen consisting of cyclophosphamide and filgrastim (Neupogen; G-CSF), followed by a second leukapheresis for collection of peripheral blood stem cells. Patients will be treated with a standard high-dose chemotherapy regimen for multiple myeloma consisting of single agent melphalan (200mg/m2). Patients will then receive their peripheral blood stem cells followed by post-transplant filgrastim for neutrophil recovery. Three days (Day 3) following stem cell infusion, patients will receive a single dose Xcellerated T Cells.