Evaluating Efficacy of Tivozanib (AV-951) in Biliary Tract Cancers

Background: Cholangiocarcinoma (CCA) is an aggressive cancer of the bile ducts. People with CCA have few treatment options and poor survival. Researchers want to see if a new drug can stop or slow CCA growth. Objective: To find the safest and most effective dose of tivozanib to treat CCA and learn its overall response rate. Eligibility: Adults ages 18 and older with CCA not removable with surgery and have been treated with at least one type of chemotherapy. Design: Participants will be screened with the following: * Medical history * Physical exam * Assessment of their ability to do daily activities * Medicine review * Blood tests, including thyroid function tests * Urine tests * Electrocardiogram, to check heart function * Pregnancy test, if needed * Tumor biopsy, if needed * Computed tomography scans * Magnetic resonance imaging, if needed Some screening tests may be repeated during the study. Participants will be asked to enroll in protocol #13C0176. This will allow any remaining tumor or blood samples to be used in future research. Participants will take tivozanib by mouth, once a day for 21 days per cycle or every other day per cycle. Each cycle is 28 days. They can take the drug until they have bad side effects, their CCA gets worse, or if they become pregnant. They will record their blood pressure twice daily at home. They will also keep a medication diary of each dose of tivozanib they take and any side effects. Participants will have study visits before starting each new cycle and every 8 weeks. They will also have a follow-up visit 30 days after treatment ends at NIH, or if they are unable to come to NIH by phone, videocall, or other NIH-approved platform. Then they will be contacted 6 and 12 months later, and then once a year.