This pilot trial will examine the feasibility of administering induction high-dose therapy with antimetabolites, followed with consolidation using high-dose single alkylating agent therapy and finally intensification therapy with sequential cycles of very high doses of the natural products (paclitaxel followed by doxorubicin) to patients with metastatic breast cancer (stage IV), and to patients with lesser stage disease at high risk for relapse (patients with four or more positive nodes (stage II), locally advanced breast cancer (stage III)), and patients with locally or regionally recurrent breast cancer.