OUTLINE: This is a randomized, placebo controlled, blinded study. Patients are randomly assigned to one of three treatment arms. All patients undergo mobilization of peripheral blood stem cells (PBSC) using cyclophosphamide IV over 1 hour and paclitaxel IV over 3 hours on day 1, and filgrastim (G-CSF) subcutaneously beginning on day 4 and continuing until completion of leukapheresis. PBSC and bone marrow cells are collected and CD34 positive cells are then selected. About 4 weeks later, patients receive high dose chemotherapy. Cyclophosphamide IV over 24 hours, carboplatin IV over 24 hours, and thiotepa IV over 24 hours are administered on days -7 to -4. Patients then receive placebo or one of two doses of expanded mesenchymal stem cells (Stromagen) IV on day -1 and CD34+ selected PBSC IV over 2 hours on day 0. Patients are followed at 6 weeks and 12 weeks, than at 1 year.