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 cell products or other recombinant human antibodies
* No history of allergic reactions attributed to compounds of similar chemical or biological composition to other agents used in the study
* No serious or nonhealing wound, ulcer, or bone fracture
* No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 28 days
* No significant traumatic injury within the past 28 days
* No clinically significant cardiovascular disease, including any of the following:

  * Myocardial infarction, coronary artery bypass graft, or unstable angina pectoris within the past 6 months
  * New York Heart Association class III or IV congestive heart failure
  * Serious cardiac arrhythmia requiring medication
  * Clinically significant peripheral vascular disease within the past 6 months
  * Cerebrovascular accident within the past 6 months
  * Pulmonary embolism, deep vein thrombosis, or other thromboembolic event within the past 6 months
  * Uncontrolled hypertension, defined as blood pressure (BP) \> 150/100 mm Hg or systolic BP \> 180 mm Hg (if diastolic BP \< 90 mm Hg) within the past 3 months
* No evidence of bleeding diathesis or coagulopathy
* No uncontrolled intercurrent illness, including, but not limited to, any of the following:

  * Ongoing or active infection
  * Psychiatric illness or social situation that would preclude study compliance
* Recovered from prior therapy
* Prior biologic or targeted therapies allowed
* No more than 1 prior systemic chemotherapy regimen for metastatic disease
* No prior antiangiogenic therapy primarily targeting the vascular endothelial growth factor pathway
* At least 4 weeks since prior radiotherapy or systemic therapy (6 weeks for mitomycin C or nitrosoureas)
* More than 28 days since prior major surgery or open biopsy
* More than 7 days since prior core biopsy
* No concurrent major surgery
* Concurrent full-dose anticoagulants (e.g., warfarin) allowed provided all of the following criteria are met:

  * In-range INR (usually between 2 and 3) on a stable dose of oral anticoagulant or low molecular weight heparin
  * No active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices)
* No other concurrent investigational agents
* No concurrent combination antiretroviral therapy for HIV-positive patients