In this study, we will determine the appropriate cell dose to safely establish mixed chimerism following partial conditioning in patients with RRMS. The study takes a gradual approach to increasing the cell dose to achieve mixed chimerism. Each patient will receive a cell dose one unit above the dose received by the most recent safely transplanted patient. We believe this study will provide a breakthrough in the treatment of MS. The goal of this study is to evaluate the potential of safely establishing mixed chimerism to interrupt the autoimmune process and end the devastating effects of MS.