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

OBJECTIVES: * Determine the effectiveness of neoadjuvant dose intensive sequential chemotherapy, followed by surgical resection, adjuvant therapy, and tandem high dose chemotherapy and stem cell rescue in patients with inflammatory stage IIIB breast cancer. * Determine the clinical and pathological remission rate (complete, partial, and overall) following neoadjuvant dose dependent sequential chemotherapy in patients with inflammatory stage IIIB breast cancer. * Determine the relapse and survival rate of these patients with the above therapy. * Determine the potential correlations between inflammatory features and hereditary background. OUTLINE: Patients are stratified according to those who have had no more than 1 cycle of neoadjuvant chemotherapy (stratum 1) and those who have had more than 1 cycle of neoadjuvant chemotherapy and/or modified radical mastectomy (stratum 2). Patients in stratum 1 receive doxorubicin IV over 96 hours on days 1-4, 15-19, and 29-32. Paclitaxel is infused over 96 hours on days 43-47 and 57-60. Filgrastim (G-CSF) is administered on days 5-10, 20-25, 33-38, 48-55, and 61-68, and beyond if the granulocyte count is less than 1000/mm\^3. A modified radical mastectomy is performed between days 70 and 80. All stratum 1 and stratum 2 patients then receive paclitaxel IV for 96 hours on days 100-104, and cyclophosphamide IV on day 121. Filgrastim is administered at one dose on days 105-110 and days 122-127 and at a higher dose on days 110-116 and days 128-135. Stem cells are harvested from the patient on days 113-116 and days 132-135. High-dose chemotherapy is then administered to all patients in the study. Course 1 starts with doxorubicin IV on days -7 to -3. Paclitaxel IV is administered for 24 hours on day -2. Filgrastim is administered by IV on day -1 and continued until the granulocyte count is greater than 1000/mm\^3 for 3 days. Peripheral stem cells are reinfused on day 0. Course 2 starts 4-6 weeks after the start of course 1 with melphalan and cisplatin being infused on day -11. Filgrastim is administered IV on days -10 to -6. Melphalan and cisplatin are administered again on day -4. Stem cells are infused on day -3 and on day 0. Filgrastim is then administered until the granulocyte count is at least 1000/mm\^3 for 3 days. Radiation therapy is started 4-7 weeks after the beginning of course 2. Tamoxifen is started within 2 weeks of discharge following course 2 in patients with hormone receptor positive tumors. Patients are followed every 3 months for two years and then annually for the next three years. PROJECTED ACCRUAL: Approximately 60 patients will be accrued, at a rate of about 15 per year.