Trifluridine/Tipiracil + Oxaliplatin in Participants With Advanced or Metastatic Biliary Tract Cancer

Inclusion Criteria: * Participants must have histologically or cytologically confirmed biliary tract cancer (BTC) including cholangiocarcinoma and gallbladder carcinoma. Individuals with ampullary cancers will not be considered eligible. Cancer must be advanced stage or metastatic. * Participants must have received only one line of systemic therapy for advanced or metastatic BTCs. * Note: Individuals who have either progressed or are intolerant to the prior therapy can be included in this study. * Age \>18 years on day of signing informed consent. Because no dosing or adverse event data are currently available on the use of FTD/TPI in individuals ≤18 years of age, children are excluded from this study. * Performance status: ECOG performance status of 0 or 1. * At least one index lesion is measurable based on RECIST 1.1. * Participants must have organ and marrow function as defined below: * Absolute neutrophil count ≥ 1,500/mcL * Platelet count ≥75,000/mcL * AST (SGOT) ≤ 2.5 X institutional upper limit of normal or ≤ 5 × ULN for participants with liver metastases * ALT (SGPT) ≤ 2.5 X institutional upper limit of normal or ≤ 5 × ULN for participants with liver metastases * Total bilirubin ≤ 1.5 × ULN or direct bilirubin ≤ ULN for participants with bilirubin levels \>1.5 x ULN * Serum Creatinine ≤ 1.5 x upper limit of normal (ULN) or creatinine clearance ≥60 mL/min for participants with creatinine levels \>1.5 x ULN (Cockcroft-Gault method) * Participants must have recovered adequately from any major surgery, prior to starting therapy. * Participants must have the ability to understand and the willingness to sign a written informed consent document. * Agree to use adequate method of contraception. Exclusion Criteria: * Participants receiving any other investigational agents. * Participant has received investigational therapy within 4 weeks or within 5 half-lives of the therapeutic agent (whichever is shorter). * Received more than one line of systemic therapy for bile duct cancer. Adjuvant therapy will not be counted as line of systemic therapy. * Receiving systemic steroid therapy (\>10mg prednisone or equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. * Prior treatment with FTD/TPI or oxaliplatin. * Known additional malignancy that currently requires active treatment. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has already undergone potentially curative therapy. * Known central nervous system metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are stable without evidence of new or enlarging brain metastases and are not using steroids for at least 7 days prior to trial treatment. * Active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids (\> 10 mg/day or equivalent of prednisone) or immunosuppressive agents. (thyroid disease and diabetes are allowed) * Interstitial lung disease or active, non-infectious pneumonitis. * Active infection requiring systemic antibiotics. * History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the individual's participation for the full duration of the trial, or is not in the best interest of the individual to participate, in the opinion of the treating investigator. * Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial, in the opinion of the treating investigator. * Participants with uncontrolled intercurrent illness including, but not limited to symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations/substance abuse disorders that would limit compliance with study requirements. * Participants pregnant or breastfeeding expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 5 months after the last dose of trial treatment. Pregnant or breastfeeding women are excluded from this study because it is unknown if the combination of FTD/TPI and oxaliplatin create the potential for teratogenic or abortifacient effects. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother with the study drug combination, breastfeeding should be discontinued if the mother is enrolled on this trial.