OUTLINE: This is a dose escalation study. Autologous blood cells are collected after completion of neoadjuvant/induction chemotherapy (and salvage mastectomy, if indicated). Patients receive IV amifostine, mitoxantrone, and thiotepa on day -7. On day -6, patients receive IV amifostine, thiotepa, and cyclophosphamide treatment. On days -5, -4, and -3, IV amifostine and cyclophosphamide are administered to participants. Following high dose chemotherapy treatment, patients rest on days -2 and -1. On day 0, patients undergo autologous blood cell transplantation. Cohorts of 3 patients each receive escalating doses of mitoxantrone and cyclophosphamide. If 1 of 3 patients at a given dose level experiences dose limiting toxicity (DLT), an additional 3 patients are treated at that dose. If at least 3 of 6 patients experience DLT at a given dose level, then the maximum tolerated dose is the previous dose level. Patients are followed at day 100, then every 6 months for 2 years, then annually until death.