VEGF Trap in Treating Patients With Recurrent, Locally Advanced, or Metastatic Cancer of the Urothelium

Inclusion Criteria: * Histologically confirmed transitional cell carcinoma (TCC) of the urothelium * Must have predominance of transitional histology, but foci of squamous and/or adenocarcinoma histology allowed * Poorly differentiated transitional cell carcinoma allowed * TCC of any of the following sites allowed: * Bladder * Renal pelvis * Ureter * Urethra * Measurable disease, defined as \>= 1 unidimensionally measurable lesion \>= 20 mm by conventional techniques OR \>= 10 mm by spiral CT scan * Locoregionally advanced or metastatic disease that is not amenable to curative surgery and/or radiotherapy * Must have received 1 prior systemic chemotherapy regimen containing a platinum compound (e.g., cisplatin, carboplatin, or oxaliplatin) in the neoadjuvant, adjuvant, or metastatic setting * No evidence of CNS disease, including primary brain tumor or brain metastases * ECOG performance status 0-2 * Absolute neutrophil count \>= 1,000/mm\^3 * Platelet count \>= 75,000/mm\^3 * Bilirubin =\< 1.5 times upper limit of normal (ULN) * AST or ALT =\< 2.5 times ULN * Creatinine =\< 2.5 times ULN OR creatinine clearance =\> 40 mL/min * Urine protein: creatinine ratio =\< 1 OR 24-hour urine protein \< 500 mg * INR =\< 1.5 (unless on full-dose warfarin) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for \>= 6 months after completion of study treatment * No known hypersensitivity to Chinese hamster ovary c…