This phase II trial is studying how well sorafenib works in treating patients with progressive regional or metastatic cancer of the urothelium. Sorafenib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth and by blocking blood flow to the tumor.

PRIMARY OBJECTIVES:

I. To evaluate the 4-month progression-free survival rate, response rate and toxicity of BAY 43-9006 in patients with progressing regional or metastatic transitional cell carcinoma (or mixed histologies containing a component of TCC) of the urothelium who have progressed on one and only one prior systemic chemotherapy regimen for metastatic disease.

SECONDARY OBJECTIVES:

I. To determine the time to disease progression and overall survival with BAY 43-9006.

II. To evaluate the frequency of polymorphisms in drug metabolizing enzymes and to correlate these polymorphisms with variations in BAY 43-9006 pharmacokinetics.

III. To evaluate the frequency of raf kinase mutations in tumor specimens and correlate these with response rate.

IV. To evaluate serum VEGF levels as potential markers of angiogenesis inhibition by BAY 43-9006.

V. To evaluate markers of apoptosis and kinase inhibition in peripheral blood mononuclear cells as potential biomarkers of BAY 43-9006 activity.

VI. To determine if there are proteins differentially translated from the genome in patients who respond to treatment with BAY 43-9006 versus patients who do not respond to BAY 43-9006.

OUTLINE: This is a multicenter study.

Patients receive oral sorafenib twice daily on days 1-56. Courses repeat every 56 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed every 3 months until 2 years from study entry and then every 6 months until 3 years from study entry.

Inclusion Criteria:

• Histologically confirmed transitional cell carcinoma or mixed histologies containing a component of transitional cell carcinoma of the urothelium (renal pelvis, ureter, bladder, urethra) with manifestations of progressing regional or metastatic cancer; or (2) Nontransitional cell histologies include patients with adenocarcinoma or squamous cell carcinomas representing greater than 90% of specimen; patients with small cell carcinoma, soft tissue sarcomas, or carcinosarcomas are excluded
• Measurable disease, as defined in the RECIST criteria; all sites of disease must be evaluated within 4 weeks prior to registration
• Patients must have progressed on one and only one prior systemic chemotherapy for metastatic disease; prior chemotherapy administered in the adjuvant or neoadjuvant setting is permitted (i.e. does not count as 1 prior regimen) provided that it was completed greater than 12 months prior to the start of the first chemotherapy regimen administered in the metastatic setting
• Patients must not have had prior systemic biologic response modifier therapy; patients must not have had chemotherapy, hormonal or biologic therapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or have recovered from adverse events due to agents administered more than 4 weeks earlier
• Prior radiotherapy is allowed; patients must be >= 2 weeks post-radiotherapy at time of registration; a previously irradiated lesion can only be used as a marker lesion if there is unequivocal evidence of progression demonstrated on serial imaging studies; patients must have recovered from all toxicities associated with prior radiotherapy
• Patients must be >= 4 weeks post-major surgery at time of registration; patients must have recovered from all toxicities associated with prior surgery
• ECOG performance status of 0 or 1
• No history of severe cardiovascular disease (AHA Class III or IV), uncontrolled CHF, uncontrolled hypertension, or ventricular dysrhythmias
• Patients with previously resected and irradiated CNS metastases with evidence of stable disease are eligible
• Patients with a history of prior malignancy are eligible provided they were treated with curative intent and have been disease free for >= 5 years; curatively treated basal cell or squamous cell carcinoma of the skin or carcinoma-in-situ of the cervix must have been treated with curative intent; patients with clinically unsuspected organ confined prostate cancer found at the time of cystoprostatectomy are eligible
• Creatinine < 1.5 mg/dL
• Granulocytes >= 1500/mm^3
• Platelets >= 100,000/mm^3
• AST =< 2.5 x institutional upper limit of normal
• Bilirubin < 1.5 mg/dl
• No active unresolved infection requiring parenteral antibiotics < 7 days prior to study entry
• Patients must not have a swallowing dysfunction which would prevent the ingesting of pills
• Patients must not have any evidence of bleeding diathesis
• Patients must not be on therapeutic anticoagulation; prophylactic anticoagulation (i.e. low dose warfarin) of venous or arterial access devices is allowed provided that the requirements for PT, INR or PTT are met
• Patients must not be taking the cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine, and phenobarbital), rifampin, or St. John's Wort
• Women of childbearing potential must not be pregnant (as proven by a negative pregnancy test within 14 days prior to registration) or breast feeding because the effects of this treatment on the fetus and breast-fed infants is unknown
• Women of childbearing potential and sexually active males must be strongly advised to use an accepted and effective method of contraception