A Phase 2 Trial of Regorafenib as A Single Agent in Advanced and Metastatic Biliary Tract Carcinoma/Cholangiocarcinoma Patients Who Have Failed First-line Chemotherapy

Inclusion Criteria: * Histologically or cytologically confirmed diagnosis of biliary tract adenocarcinoma/cholangiocarcinoma (including primary intra- and extrahepatic diseases); pathologic confirmation may be from the primary or a metastatic site * Must have locally advanced or distant metastatic disease that is not surgically curable * Failed first-line chemotherapy (including systemic and local-regional therapy). * Age ≥ 18 years. * Life expectancy of at least ≥ 12 weeks (3 months). * Performance status ECOG ≤ 1 * Adequate liver, kidney, and bone marrow function as assessed by the following laboratory requirements: * Total bilirubin ≤ 3.0 x the upper limit of normal (ULN) (biliary stenting or percutaneous biliary drainage are allowed for cancer related biliary obstruction) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 5.0 x ULN * Alkaline phosphastase limit ≤ 2.5 x ULN (≤ 5.0 x ULN for subjects with intrahepatic involvement of their cancer) * Serum creatinine ≤ 1.5 x the ULN * International normalized ratio (INR)/partial thromboplastin time (PTT) ≤ 1.5 x ULN. (Patients who are therapeutically 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 ≥ 75,000 /mm3 * Hemoglobin (Hb) ≥ 9 g/dL, * Absolute neutrophil count (ANC) ≥ 1500/mm3. * Blood transfusion to meet the inclusion criteria will not be allowed. * 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. * Patients (men and women) of childbearing potential must agree to use Double Barrier method of birth control beginning at the signing of the ICF until at least 3 months after the last dose of study drug. * Patients must be able to swallow and retain oral medication. * Patients must be able to understand and be willing to sign the written informed consent form. A signed informed consent form must be appropriately obtained prior to the conduct of any trial-specific procedure. Exclusion Criteria: * 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 ≥ Grade 3 within 4 weeks prior to prior to registration. * Patients 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 the study registration. * Previous exposure to Vascular endothelial growth factor (VEGF) inhibitor(s), * Patients with any previously untreated or concurrent cancer that is distinct in primary site or histology from biliary tract cancer except cervical cancer in-situ, treated basal cell carcinoma, or superficial bladder tumor. Patients surviving a cancer that was curatively treated and without evidence of disease for more than 3 years prior to registration are allowed. All cancer treatments must be completed at least 3 years prior to prior to registration). * Patients with phaeochromocytoma. * 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. * 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 * Patients with seizure disorder requiring medication. * Proteinuria ≥ Grade 3 (\> 3.5 g/24 hours, measured by urine protein: creatinine ratio on a random urine sample). * Active signs and symptoms of interstitial lung disease pleural effusion or ascites that causes respiratory compromise (≥ Grade 2 dyspnea). * History of organ allograft (including corneal transplant). * Known or suspected allergy or hypersensitivity to any of the study drug classes. * 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. * Concurrent anti-cancer therapy (chemotherapy, radiation therapy, surgery, immunotherapy, biologic therapy, or tumor embolization) other than study treatment regorafenib. However, the palliative external beam radiation therapy (XRT) to non-targeted lesions is allowed. * Prior use of regorafenib. * Concurrent use of another investigational drug or device therapy (i.e., outside of study treatment) during, or within 28 days prior to registration * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to registration (biliary stenting or percutaneous biliary drainage are not included). * Use of any herbal remedy (e.g. St. John's Wort \[Hypericum perforatum\])