In ITN033AI, high-dose chemotherapy with autologous CD34-selected hematopoietic cell transplantation will be given to confirm the results from the pilot study and to offer therapy to patients with early MS and a poor prognosis. Research studies will be performed in addition to clinical assessments to better understand the effect of the treatment on the activity of MS. High-dose chemotherapy will be used to deplete autoreactive immune cells. These regimens also deplete the bone marrow, the source of blood-forming CD34+ stem cells which causes very low blood counts. Therefore, the participant's autologous CD34+ hematopoietic stem cells will be collected before high dose immunosuppressive therapy is given and then returned as a transplant post-chemotherapy. Patients will be followed closely after the autologous transplantation since they will be at risk for infections after treatment.