Erlotinib, Trastuzumab, and Paclitaxel in Treating Patients With Advanced Solid Tumors

Inclusion Criteria: * Histologically confirmed metastatic solid tumor for which there are no effective standard treatment options * HER2 positive (1+ to 3+) * Tumor has a high likelihood of expressing epidermal growth factor receptor (EGFR) * No evidence of leptomeningeal disease or brain metastases unless previously treated, currently asymptomatic, and off both antiepileptics and dexamethasone * Patients with treated brain metastases are eligible if they are without any clinical change in their brain disease status for at least 4 weeks after whole brain irradiation * Performance status - ECOG 0-2 * Performance status - Karnofsky 60-100% * At least 12 weeks * Absolute neutrophil count at least 1,500/mm\^3 * Platelet count at least 100,000/mm\^3 * Bilirubin normal * AST/ALT no greater than 2.5 times upper limit of normal (ULN) (5 times ULN if liver has tumor involvement) * Creatinine normal * Creatinine clearance at least 60 mL/min * LVEF more than 50% by radionuclide ventriculogram or MUGA scan * No significant cardiovascular disease * No prior congestive heart failure requiring therapy * No unstable angina pectoris * No myocardial infarction within the past 6 months * No gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation * Patients who are unable to swallow tablets and/or who have silicon-based G-tubes may dissolve the tablets in distilled water * No active peptic ulcer disease * HIV negative * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No known or suspected hypersensitivity to paclitaxel * No prior allergic reactions attributed to compounds of similar chemical or biologic composition to erlotinib or other study agents * No concurrent active infection * No other concurrent medical condition that would preclude study participation * No persistent grade 2 or greater neurotoxicity/neuropathy from any cause * No psychiatric disorders or altered mental status that would preclude study participation * No other concurrent immunotherapy * No concurrent cytokine growth factors (e.g., colony-stimulating factors) * At least 4 weeks since prior chemotherapy (6 weeks for mitomycin or nitrosoureas) and recovered * No other concurrent chemotherapy * See Disease Characteristics * No concurrent hormonal therapy except megestrol as an appetite stimulant or luteinizing hormone-releasing hormone agonists for prostate cancer * See Disease Characteristics * No concurrent radiotherapy * No prior surgical procedures affecting absorption * No prior EGFR-targeting therapy * No other concurrent experimental medications or other specific antitumor therapy * No concurrent immunosuppressant therapy * No concurrent antiarrhythmic therapy for a ventricular arrhythmia