Gefitinib, Trastuzumab, and Docetaxel in Treating Patients With Metastatic Breast Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed adenocarcinoma of the breast * Metastatic disease * HER-2/neu overexpression (3+ by immunohistochemistry OR 2+ by fluorescence in situ hybridization) * Measurable or evaluable disease * Hormone receptor status: * Not specified PATIENT CHARACTERISTICS: Age * 18 and over Sex * Male or female Menopausal status * Not specified Performance status * ECOG 0-2 Life expectancy * Not specified Hematopoietic * Absolute granulocyte count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 Hepatic * AST and ALT \< 2.5 times upper limit of normal (ULN) (5.0 times ULN in the presence of liver metastases) * Bilirubin \< 1.5 times ULN * No unstable or uncompensated hepatic disease Renal * Creatinine \< 1.6 mg/dL * No unstable or uncompensated renal disease Cardiovascular * LVEF \> 45% by echocardiogram or MUGA * No prior New York Heart Association class I-IV heart disease * No prolonged PR interval or atrioventricular block on ECG * No unstable or uncompensated cardiac disease Pulmonary * No unstable or uncompensated respiratory disease * No clinically active interstitial lung disease * Patients who are asymptomatic and have chronic stable radiographic changes are allowed Immunologic * No autoimmune disorders * No conditions of immunosuppression * No severe hypersensitivity to taxane or gefitinib or any of its excipients Other * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No other prior or concurrent malignancy within the past 5 years except basal cell carcinoma or carcinoma in situ of the cervix * No other severe or uncontrolled systemic disease * No other acute or chronic medical condition that would preclude study participation * No other significant clinical disorder or laboratory finding that would preclude study participation * No psychiatric illness that would preclude study compliance PRIOR CONCURRENT THERAPY: Biologic therapy * Prior adjuvant trastuzumab (Herceptin®) allowed if \> 6 months elapsed before disease recurrence * No prior trastuzumab for metastatic breast cancer * No prior monoclonal antibodies directed at the epidermal growth factor receptor (EGFR) Chemotherapy * Prior adjuvant chemotherapy (or as first-line therapy for metastatic breast cancer) allowed * Prior adjuvant taxane allowed if completed \> 6 months before diagnosis of metastatic breast cancer * No prior docetaxel for metastatic breast cancer Endocrine therapy * Prior adjuvant hormonal therapy (or as first-line therapy for metastatic breast cancer) allowed * No concurrent hormonal therapy * Concurrent steroids allowed provided dose is stable Radiotherapy * Not specified Surgery * Fully recovered from prior oncologic or other major surgery * No concurrent surgery within 7 days of gefitinib administration Other * Recovered from prior anticancer therapy (alopecia allowed) * More than 30 days since prior non-approved drug or investigational agent * No other prior EGFR-directed therapy (i.e., tyrosine kinase inhibitors) * No concurrent use of any of the following medications: * Phenytoin * Carbamazepine * Barbiturates * Rifampin * Hypericum perforatum (St. John's wort) * No other concurrent anticancer therapy * No concurrent cardioprotective drugs * No concurrent oral retinoids * Concurrent participation in the City of Hope indium-labeled trastuzumab imaging study allowed