Study of Regorafenib for Urothelial Cancer Following Chemotherapy (UAB 1477)

Inclusion Criteria: * Patients must have pathologically or cytologically proven transitional cell carcinoma of the urothelium. * Progressive disease after 1-3 prior chemotherapy regimens (perioperative chemotherapy within 12 months will be considered one regimen). * Prior regimen must be within 6 months of registration * Measurable disease by RECIST 1.1 * Eastern Cooperative Oncology Group (ECOG) Performance status 0-1 * Patients with metastatic (lymph node or distant metastasis, i.e. N+ or M1) or locally advanced unresectable (T4b) transitional cell carcinoma. * Age ≥19 years * Life expectancy of at least 12 weeks (3 months) * Subjects must be able to understand and be willing to sign the written informed consent form. * Adequate bone marrow, liver and renal function as assessed by the following laboratory requirements: * Total bilirubin ≤ 1.5 x the upper limits of normal (ULN) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) less than or equal to 2.5 x ULN (≤ 5 x ULN for subjects with liver involvement of their cancer) * Alkaline phosphatase limit ≤ 2.5 x ULN (≤ 5 x ULN for subjects with liver involvement of their cancer) * Serum creatinine ≤ 1.5 x the ULN * International normalized ratio (INR) less than or equal to 1.5 x ULN. (Subjects who are prophylactically treated with an agent such as warfarin or heparin will be allowed to participate provided that no prior evidence of underlying abnormality in coagulation parameters exists.Close monitoring of at least weekly evaluations will be performed until INR/PTT is stable based on a measurement that is pre-dose as defined by the local standard of care. * Platelet count \>100,000/mm3, hemoglobin (Hb) \>8 g/dL, absolute neutrophil count (ANC) 1500/mm3. The patient cannot be transfused in order to meet study entry criteria. * Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of study drug. Post- menopausal women (defined as no menses for at least 1 year) and surgically sterilized women are not required to undergo a pregnancy test. The definition of adequate contraception will be based on the judgment of the investigator. * Subjects (men and women) of childbearing potential must agree to use adequate contraception beginning at the signing of the informed consent form until at least 3 months after the last dose of study drug. The definition of adequate contraception will be based on the judgment of the principal investigator or a designated associate. * Subject must be able to swallow and retain oral medication. Exclusion Criteria: * Component of small-cell cancer or sarcomatoid cancer * Prior therapy with any systemic therapy (chemotherapy or biologic therapy) within twenty-eight days prior to study entry * Patients must have recovered from toxicities from prior systemic anticancer treatment or local therapies. * Patients who have undergone major surgery \<4 weeks or minor surgery \<2 weeks prior to registration. Wounds must be completely healed prior to study entry and patients recovered from all toxicities from surgery. Placement of a vascular access device is not considered major or minor surgery in this regard. * Prior radiation therapy is allowed as long as the irradiated area was not the sole source of measurable disease and radiotherapy was completed with recovery from toxicity, at least three weeks prior to enrollment. If the irradiated area is the only site of disease, there must be evidence of progressive disease. * Uncontrolled central nervous system (CNS) metastases (previously treated with radiation and off steroids is acceptable). * Patient with active or uncontrolled infection. * Recent or active bleeding diathesis or arterial vascular event within 4 weeks. * Pregnant or nursing (Fertile patients must use effective contraception during and for up to 3 months after completion of study treatment.) * Patients may not be receiving any other investigational agents. * Previous assignment to treatment during this study. Subjects permanently withdrawn from study participation will not be allowed to re-enter study. * Uncontrolled hypertension (systolic pressure \>140 mm Hg or diastolic pressure \>90 mm Hg on repeated measurement) despite optimal medical management. * Active or clinically significant cardiac disease including: * Congestive heart failure - New York Heart Association (NYHA) Class II. * Active coronary artery disease. * Cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers or digoxin. * Unstable angina (angina symptoms at rest), new-onset angina within 3 months before randomization, or myocardial infarction within 6 months before randomization. * Evidence or history of bleeding diathesis or coagulopathy. * Any hemorrhage or bleeding event ≥ NCI CTCAE Grade 3 within 4 weeks prior to start of study medication. * Subjects with thrombotic, embolic, venous, or arterial events, such as cerebrovascular accident (including transient ischemic attacks) deep vein thrombosis or pulmonary embolism within 6 months of start of study treatment within 6 months of informed consent. * Subjects with any previously untreated or concurrent cancer that is distinct in primary site or histology from breast cancer except cervical cancer in-situ, treated localized basal cell carcinoma, Gleason score 6 prostate cancer or superficial bladder tumor. Subjects surviving a cancer that was curatively treated and without evidence of disease for more than 3 years before randomization are allowed. All cancer treatments for another malignancy must be completed at least 3 years prior to study entry (i.e., signature date of the informed consent form). * Patients with pheochromocytoma. * Known history of human immunodeficiency virus (HIV) infection or current chronic or active hepatitis B or C infection requiring treatment with antiviral therapy. * Ongoing infection \>Grade 2 NCI-CTCAE v4.0. * Symptomatic metastatic brain or meningeal tumors. * Presence of a non-healing wound, non-healing ulcer, or bone fracture. * Renal failure requiring hemo-or peritoneal dialysis. * Dehydration Grade \>1 NCI-CTCAE v4.0. * Patients with seizure disorder requiring medication. * Persistent proteinuria greater than or equal to Grade 3 NCI-CTCAE v4.0 (\> 3.5 g/24 hrs, measured by urine protein:creatinine ratio on a random urine sample). * Interstitial lung disease with ongoing signs and symptoms at the time of informed consent. * Pleural effusion or ascites that causes respiratory compromise (≥ NCI- CTCAE version 4.0 Grade 2 dyspnea). * History of organ allograft (including corneal transplant). * Known or suspected allergy or hypersensitivity to any of the study drugs, study drug classes, or excipients of the formulations given during the course of this trial. * Any malabsorption condition. * Women who are pregnant or breast-feeding. * Any condition which, in the investigator's opinion, makes the subject unsuitable for trial participation. * Substance abuse, medical, psychological or social conditions that may interfere with the subject's participation in the study or evaluation of the study results.