Gefitinib Plus Combination Chemotherapy in Treating Patients With Locally Advanced or Metastatic Bladder Cancer

Inclusion Criteria: * Biopsy proven transitional cell carcinoma of the urothelial tract (bladder, ureter, renal pelvis or urethra); histologic documentation of metastatic/recurrent disease is not required; clinical, but not pathologic staging, is required * Metastatic (N2, N3 or M1) urothelial tract carcinoma; patients must not be candidates for potentially curative surgery or radiation therapy * Patients must have measurable disease as defined below: * Measurable disease: lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan; the bladder is not a site of measurable disease * Non-measurable disease: all other lesions, including small lesions (longest diameter \< 20 mm with conventional techniques or \< 10 mm with spiral CT scan) and truly non-measurable lesions; lesions that are considered non-measurable include the following: * Bone lesions * Leptomeningeal disease * Ascites * Pleural/pericardial effusion * Inflammatory breast disease * Lymphangitis cutis/pulmonis * Abdominal masses that are not confirmed and followed by imaging techniques * Cystic lesions * Prior treatment: * No prior systemic chemotherapy except single-agent chemotherapy used as a radiosensitization agent; prior intravesical chemotherapy is permissible; prior adjuvant or neoadjuvant chemotherapy is not permissible * No prior systemic therapy for advanced urothelial carcinoma including investigational therapies such as, but not limited to, agents targeting the HER2/neu, signal transduction (including EGFR), angiogenic, immune, and cell cycle pathways * No prior treatment with ZD1839 * \> 4 weeks and fully recovered from major surgery, radiation, or intravesical chemotherapy * Tumor tissue from the primary tumor or from biopsy of a metastatic site must be available for EGFR expression determination; when tissue specimens from both primary and metastatic sites are available, both must be submitted for EGFR testing; expression of EGFR is not required * No cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) inducers within 7 days prior to starting protocol therapy and while on protocol treatment; CYP3A4 inducers include phenytoin, carbamazepine, barbiturates, rifampin, St John's Wort, dexamethasone, modafinil, and rifapentine; single doses of dexamethasone used as an antiemetic are permitted * No evidence of brain metastases * Patient must have no evidence of: * \> grade 1 pre-existing sensory or motor neuropathy * Active severe chronic gastrointestinal disorders including liver disease, diarrheal or emetic disorders, or malabsorptive conditions causing nausea or diarrhea * Active severe chronic desquamative cutaneous disorder * Active severe corneal disease or inflammatory ocular disorder * No "currently active" second malignancy other than non-melanoma skin cancers; patients are not considered to have a "currently active" malignancy if they have completed therapy and considered by their physician to be at less than 30% risk of relapse * No patients with uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * No human immunodeficiency virus (HIV) disease * Common Toxicity Criteria (CTC) (Eastern Cooperative Oncology Group \[ECOG\]) performance status 0-2 * Granulocytes \>= 1,500/ul * Platelet count \>= 100,000/ul * Bilirubin =\< 1.25 x upper limits of normal * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.0 x upper limits of normal * Calculated creatinine clearance \>= 50 ml/min Exclusion Criteria: * Patients must not be pregnant or engaged in nursing; men and women of reproductive age must agree to practice effective contraception in order to participate in this study