Chemotherapy and Stem Cell Transplantation in Treating Patients With Stage IIIB Breast Cancer

DISEASE CHARACTERISTICS: * Histologically proven stage IIIB breast cancer with dermal/epidermal invasion or clinical features of inflammation, erythema, pain or hypersensitivity, edema, or thickening of the skin * Diagnosis within the past 6 months PATIENT CHARACTERISTICS: Age: * 60 and under Performance status: * Karnofsky 80-100% Life expectancy: * Not specified Hematopoietic: * Absolute neutrophil count at least 1,500/mm\^3 * Platelet count at least 100,000/mm\^3 Hepatic: * Bilirubin less than 1.5 mg/dL * SGOT or SGPT no greater than 1.5 times the upper limit of normal Renal: * Creatinine less than 1.2 mg/dL * Creatinine clearance at least 80 mL/min * No history of hemorrhagic cystitis Cardiovascular: * Left ventricular fraction at least 55% on MUGA scan * No previous valvular heart disease or arrhythmia Pulmonary: * FEV\_1 at least 60% predicted * Room air pO\_2 greater than 85 mmHg * Room air pCO\_2 no greater than 43 mmHg * DLCO at least 60% of the lower limit of predicted value Other: * No history of malignant disease in the past 5 years, except for squamous or basal cell skin cancer and stage I or in situ cervical cancer * No organic CNS dysfunction * Not pregnant * No known and potentially disabling psychosocial history * Not positive for hepatitis B or HIV PRIOR CONCURRENT THERAPY: Biologic therapy: * Not specified Chemotherapy: * Stratum 1: * No more than one cycle of chemotherapy * Stratum 2: * No greater than 225 mg/m\^2 doxorubicin…