RATIONALE: Drugs used in chemotherapy use different ways to stop tumor cells from dividing so they stop growing or die. Combining chemotherapy with peripheral stem cell transplantation may allow the doctor to give higher doses of chemotherapy drugs and kill more tumor cells.

PURPOSE: Phase I trial to study the effectiveness of combination chemotherapy followed by peripheral stem cell transplantation in treating patients who have stage III or stage IV breast cancer.

OBJECTIVES: I. Determine the maximum tolerated dose of paclitaxel when combined with high dose cyclophosphamide and thiotepa followed by autologous peripheral blood stem cell transplantation and radiotherapy in patients with advanced breast cancer. II. Assess the overall safety and toxicity of this regimen in these patients.

OUTLINE: This is a dose escalation study of paclitaxel. Mobilization and harvest: Patients undergo mobilization of peripheral blood stem cells (PBSC) according to the protocol currently used or patients may be mobilized using cytokines alone or chemomobilization at the discretion of the attending physician. PBSC are harvested and selected for CD34+ cells. If an adequate number of CD34+ cells are not harvested, autologous bone marrow may be used. Preparative regimen: Patients receive paclitaxel IV over 24 hours on day -5 and high dose thiotepa IV over 2 hours and high dose cyclophosphamide IV over 2 hours on day -6, day -4 following paclitaxel infusion, and day -2. Cohorts of 3-6 patients receive escalating doses of paclitaxel until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose preceding that at which 2 of 3 or 3 of 6 patients experience dose limiting toxicity. Transplantation: PBSC are reinfused on day 0 or a minimum of 48 hours after completion of chemotherapy. Patients receive filgrastim (G-CSF) subcutaneously beginning on day 0 and continuing until 3 days after blood counts have recovered. Sites of pretransplantation metastases greater than 3 cm are irradiated beginning after PBSC transplantation and after blood counts recover. Patients are followed every month for 1 year, then every 3 months thereafter.

PROJECTED ACCRUAL: Approximately 20 patients will be accrued for this study within 1 year.

DISEASE CHARACTERISTICS: Histologically proven stage III or IV breast cancer Must have responding disease (at least 50% reduction in the sum of the products of all diameters of measurable nonbony lesions and at least symptomatic improvement in painful bone disease) following conventional dose chemotherapy Asymptomatic patients with bony disease eligible if no new lesions or other evidence of bone progression If only bone disease present, there must be no new bony lesions following cytoreductive chemotherapy Patients who are disease free following surgery (e.g., stage III patients or solitary lymph node patients following excisional biopsy) eligible No CNS disease Hormone receptor status: Not specified

PATIENT CHARACTERISTICS: Age: Physiologic 60 and under Menopausal status: Not specified Performance status: ECOG 0 or 1 Life expectancy: Not specified Hematopoietic: Absolute neutrophil count at least 1,500/mm3 Platelet count at least 100,000/mm3 Hemoglobin at least 8.0 g/dL Hepatic: Bilirubin less than 2.5 times normal unless due to Gilbert's syndrome SGOT or SGPT less than 2.5 times normal Alkaline phosphatase less than 2.5 times normal If hepatitis C antibody positive, then liver function must be normal OR liver dysfunction must be due to metastatic disease and not chronic hepatitis Renal: Creatinine less than 1.5 mg/dL OR Creatinine clearance greater than 50 mL/min Cardiovascular: LVEF at least 50% unless cleared by cardiologist No myocardial infarction within the past 6 months No significant arrhythmia requiring medications No congestive heart failure Pulmonary: DLCO at least 50% predicted FEV1 and/or FVC at least 75% predicted unless due to neoplastic pulmonary involvement No serious nonneoplastic pulmonary disease (severe chronic obstructive lung disease) that would preclude study therapy Other: HIV negative Hepatitis B and C surface antigen negative No active serious medical condition that would preclude study therapy No allergy to Cremophor Not pregnant or nursing Negative pregnancy test

PRIOR CONCURRENT THERAPY: No more than 3 prior treatment regimens for metastatic disease Biologic therapy: Not specified Chemotherapy: See Disease Characteristics Prior conventional dose chemotherapy as adjuvant or as treatment for advanced disease allowed Prior doxorubicin greater than 450 mg/m2 allowed if dexrazoxane was used to reduce risk of cardiotoxicity At least 3 weeks since prior chemotherapy Endocrine therapy: Not specified Radiotherapy: No prior radiotherapy to indicator lesions At least 3 weeks since other prior radiotherapy Surgery: See Disease Characteristics At least 3 weeks since prior surgery