Single Agent Regorafenib in Refractory Advanced Biliary Cancers

Inclusion Criteria:

* Histologically or cytologically documented carcinoma primary to the intra- or extra-hepatic biliary system or gall bladder with clinical and/or radiologic evidence of unresectable, locally advanced or metastatic disease. Patients with ampullary carcinoma are not eligible.
* Have failed no more than 2 prior lines of systemic chemotherapy for advanced biliary cancer. Patients who received adjuvant chemotherapy and had evidence of disease recurrence within 6 months of completion of the adjuvant treatment are also eligible. If patient received adjuvant treatment and had disease recurrence after 6 months, they will only be eligible after failing one line of systemic chemotherapy used to treat the disease recurrence.
* Eastern Cooperative Oncology Group (ECOG) Performance Status Assessment of 0 or 1
* Measurable and non-measurable disease will be allowed.
* Must not have been treated with any vascular endothelial growth factor (VEGF) inhibitors. Prior 5-Fluorouracil (5-FU) or capecitabine treatment is allowed only if given as a radiosensitizer concurrently with radiation therapy at least 12 weeks prior to registration or if given as part of any adjuvant therapy regimen \> 6 months prior to study enrollment.
* Life expectancy of at least 12 weeks (3 months)
* For patients who have received prior cryotherapy, radiofrequency ablation, therasphere, ethanol injection, transarterial chemoembolization (TACE) or photodynamic therapy, the following criteria must be met: 28 days have elapsed since that therapy (lesions that have not been treated with local therapy must be present and measureable.
* Able to understand and willing to sign the written informed consent form
* All acute toxic effects of any prior treatment have resolved to National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE) v4.0 Grade 1 or less at the time of signing the Informed Consent Form (ICF).
* Adequate bone marrow and liver function
* Participants can receive 5-FU or capecitabine.
* Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of study drug.
* Men and women of childbearing potential must agree to use adequate contraception beginning at the signing of the ICF until at least 3 months after the last dose of study drug.
* Able to swallow and retain oral medication

Exclusion Criteria:

* Previous assignment to treatment during this study. Participants permanently withdrawn from study participation will not be allowed to re-enter study.
* Other investigational treatment during or within 21 days before starting study treatment
* Child Pugh B and C
* Uncontrolled hypertension (systolic pressure \>140 mm Hg or diastolic pressure \> 90 mm Hg \[NCI-CTCAE v4.0\] on repeated measurement) despite optimal medical management
* Active or clinically significant cardiac disease
* 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
* Participants 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 informed consent
* Active malignancy except for nonmelanoma skin cancer or in situ cervical cancer. Potential participants surviving a cancer that was curatively treated and without evidence of disease for more than 3 years before the trial are allowed. All cancer treatments must be completed at least 3 years prior to study entry (i.e., signature date of the informed consent form).
* Potential participants with phaeochromocytoma
* Potential participants with severe hepatic impairment (Child-Pugh Class C)
* 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
* Patients with seizure disorder requiring medication
* Persistent proteinuria \>/= Grade 3 NCI-CTCAE v4.0 (\> 3.5 g/24 hours, 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 potential participant unsuitable for trial participation
* Substance abuse, medical, psychological or social conditions that may interfere with participation in the study or evaluation of the study results