This Phase I/II clinical study is designed to examine the safety of Xcellerated T Cells, an activated, autologous T cell product, in study subjects undergoing an autologous peripheral blood stem cell transplant for the treatment of multiple myeloma. Thirty-five patients will be treated. Patients must have undergone induction therapy prior to study registration, and may not have progressed following induction therapy or any other prior therapy for myeloma.