Trastuzumab in Treating Patients With Previously Treated, Locally Advanced, or Metastatic Cancer of the Urothelium

Inclusion Criteria: * Histologically confirmed transitional cell carcinoma (TCC) of the urothelium, including the bladder, urethra, ureter, or renal pelvis * No pure adenocarcinomas, pure squamous cell carcinomas, small cell carcinoma, or only small foci of TCC (less than 10% of tumor specimen) * Locally advanced (T4b) TCC of the bladder * Metastatic (N2 or N3 or M1)TCC of the urothelium * HER2 expression (3+) as determined by immunohistochemistry or gene amplification by fluorescent in situ hybridization * Must not be a candidate for potentially curative surgery or radiotherapy * Measurable disease * At least 1 unidimensionally measurable lesion of at least 20 mm by conventional techniques OR at least 10 mm by spiral CT scan * The following lesions are considered nonmeasurable: * Bone lesions * Leptomeningeal disease * Ascites * Pleural/pericardial effusion * Lymphangitis cutis/pulmonis * Abdominal masses not confirmed and followed by imaging techniques * Cystic lesions * Primary bladder masses * Relapsed from or failed to achieve a complete or partial response after 1 prior systemic chemotherapy regimen for TCC, including cisplatin, carboplatin, paclitaxel, docetaxel, or gemcitabine * Prior adjuvant or neoadjuvant chemotherapy is considered 1 prior chemotherapy regimen * Prior single-agent chemotherapy as a radiosensitizer is not considered a prior systemic chemotherapy regimen * No known brain metastases * Performance status - CTC 0-2 * More than 12 weeks * Absolute neutrophil count at least 1,000/mm\^3 * Platelet count at least 75,000/mm\^3 * Bilirubin no greater than 2 times upper limit of normal (ULN) * AST no greater than 2 times ULN * Creatinine clearance at least 30 mL/min * Ejection fraction at least 50% (or lower limit of normal) by echocardiogram or MUGA * No history of ongoing congestive heart failure * No active cardiac ischemia * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No other prior malignancy within the past 5 years except adequately treated basal cell or squamous cell skin cancer or carcinoma in situ of the cervix * HIV negative * No known autoimmune disease * No prior trastuzumab (Herceptin) * At least 14 days since prior radiotherapy * At least 30 days since prior chemotherapy * Prior doxorubicin allowed provided cumulative dose is no greater than 300 mg/m\^2 * Prior epirubicin allowed provided cumulative dose is no greater than 600 mg/m\^2 * No concurrent chemotherapy * No concurrent hormonal therapy except: * Steroids given for adrenal failure * Hormones administered for nondisease-related conditions (e.g., insulin for diabetes) * Intermittent dexamethasone as an antiemetic or for sensitivity reactions to study drug * No concurrent palliative radiotherapy * Prior radiotherapy allowed provided treated area is not only site of measurable disease * At least 14 days since prior surgery