Chemotherapy Followed by Peripheral Stem Cell Transplantation Plus Biological Therapy in Treating Women With Stage IV Breast Cancer

DISEASE CHARACTERISTICS: Women with histologically documented metastatic carcinoma of the breast Bilateral disease allowed Concurrent intraductal or lobular carcinoma in situ allowed Measurable or evaluable recurrent metastatic disease (stage IV) documented by radiograph, CT scan, nuclear medicine scan, or physical exam Biopsy of recurrent site(s) recommended but not required Nonmeasurable disease allowed if tumor or metastatic disease has been previously removed or successfully treated 0 to 3+ HER2 amplification, as determined by FISH No clinical evidence of active brain metastases Patients with treated brain metastases (i.e., those who have received definitive radiation, chemotherapy, and/or underwent surgery) and are stable are eligible Hormone receptor status: Estrogen or progesterone receptor positive or negative PATIENT CHARACTERISTICS: Menopausal status not specified Karnofsky performance status 70-100% OR ECOG performance status 0-2 Life expectancy at least 3 months Granulocyte count at least 1,500/mm^3 Platelet count at least 50,000/mm^3 Hemoglobin greater than 8 g/dL Bilirubin less than 1.5 times normal AST, ALT, and alkaline phosphatase < 5 times upper normal Creatinine less than 1.8 mg/dL Creatinine clearance at least 60 mL/min BUN less than 1.5 times normal No myocardial infarction (MI) within the past year No history of MI (> 1 year ago) with current coronary symptoms requiring medication No current history of angina/coronary symptoms requiring medication No clinical evidence of congestive heart failure requiring medical management No significant congestive heart failure No other uncontrolled or significant cardiovascular disease Ejection fraction at least 45% at rest by MUGA Systolic BP < 130 mm Hg and diastolic BP < 80 mm Hg BP must be controlled to meet the standard by anti-hypertensive medications for at least 7 days prior to the first infusion PFT-FEV_1 at least 50% predicted DLCO2 at least 50% predicted FVC at least 50% predicted No other malignancy within the past 3 years No other serious medical or psychiatric illness that would preclude study participation HIV negative Not pregnant or nursing Negative pregnancy test Fertile patients must use effective contraception PRIOR CONCURRENT THERAPY: See Disease Characteristics Prior chemotherapy regimens allowed, including prior treatment on protocol WSU-2006-130 Prior vaccine therapy on protocol WSU-2006-130 allowed More than 4 weeks to leukapheresis since prior hormonal therapy No radiation to the axial skeleton within 4 weeks of leukapheresis No concurrent hormonal therapy for breast cancer Hormones administered for non-disease-related condition (e.g. insulin for diabetes) allowed Concurrent steroids for adrenal failure, septic shock, or pulmonary toxicity allowed