A Study of BMS-936558 With SBRT After Induction Chemotherapy in Cholangiocarcinoma

Inclusion Criteria: * Inclusion criteria: 1. Signed and dated informed consent form. 2. Patients aged ≥18 years. 3. Pathologically (histologically or cytologically) and radiologically confirmed diagnosis of non-resectable locally advanced or metastatic or recurrent intrahepatic or extrahepatic CCA within 90 days of registration. 4. Patients who have stable disease or partial response following 4 cycles of cisplatin/gemcitabine. 5. ECOG performance score \<3 o An estimated life expectancy of more than 3 months. 6. Have adequate hematologic and biochemical function by meeting the following: * Total bilirubin acceptable level ≤ 1.5 × the institutional upper limit of normal (ULN) range; * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) acceptable levels up to 5 x ULN range; * Serum urea and serum creatinine acceptable levels up to 1.5 x ULN range; * Calculated glomerular filtration rate ≥ 45 mL/min according to the Chronic Kidney Disease Epidemiology Collaboration equation (or local institutional standard method). 7. Negative serum or urine pregnancy test at screening for women of childbearing potential who are sexually active. 8. Highly effective contraception for both males and females of child-bearing potential who are sexually active throughout the study and for at least 5 months and 7 months after the last BMS-936558 treatment administration, respectively. 9. Candidate for percutaneous biopsy as per tumor location evidenced by CT scan and interventional radiologist. Exclusion Criteria: 1. Patients who have progression following 4 cycles of cisplatin/gemcitabine evidenced by CT scan as per RECIST 1.1. 2. Active brain metastases or leptomeningeal metastases. 3. Prior organ transplantation or allogenic stem-cell transplantation. 4. Known prior severe hypersensitivity to IMP or any component in its formulations, including known severe hypersensitivity reactions to monoclonal antibodies (NCI-CTCAE v4.03 Grade ≥ 3). 5. Active infection requiring systemic therapy within 28 days before the first dose of study treatment (e.g., urinary tract infection). 6. Known history of testing positive for the human immunodeficiency virus or known acquired immunodeficiency syndrome. 7. Evidence of liver cirrhosis. 8. Current use of immunosuppressive medication, except for the following: * Intranasal, inhaled, topical steroids, or local steroid injection (e.g., intra-articular injection); * Systemic corticosteroids at physiologic doses ≤ 10 mg/day of prednisone or equivalent; * Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication). 9. Active autoimmune diseases that might deteriorate upon receiving an immune-stimulatory agent. 10. Conditions such as vitiligo, psoriasis, diabetes type I, or hypo- or hyper-thyroid diseases not requiring immunosuppressive treatment are eligible. 11. Commonly excluded conditions include: Addison's disease, thyroiditis/Hashimoto's thyroiditis, systemic lupus erythematosus, Sjogren's syndrome, scleroderma, myasthenia gravis, Goodpasture's syndrome, and Grave's disease 12. Hepatic insufficiency manifesting as clinical jaundice, hepatic encephalopathy, and/or variceal bleed within 60 days prior to study entry. 13. Transmural myocardial infarction within 6 months of enrollment; provided that anti-platelets cannot be stopped to perform percutaneous biopsy. 14. Congestive heart failure (≥ New York Heart Association Classification Class II) requiring hospitalization within the last 6 months provided that anti-platelets cannot be stopped to perform percutaneous biopsy. 15. Serious cardiac arrhythmia requiring medical treatment provided that anti-platelets cannot be stopped to perform percutaneous biopsy. 16. Recent cerebral vascular accident/stroke within 6 months of enrollment provided that anti-platelets cannot be stopped to perform percutaneous biopsy. 17. End-stage renal disease requiring dialysis. 18. Other severe acute or chronic medical conditions including immune colitis, inflammatory bowel disease, immune pneumonitis, pulmonary fibrosis, or psychiatric conditions including recent (within the past year) or active suicidal ideation or behavior. 19. Vaccination within 4 weeks of the first dose of BMS-936558 and while on trial is prohibited except for administration of inactivated vaccines. 20. Treatment with an investigational agent within 28 days before the first dose of study treatment. 21. Prior treatment with any drug or antibody (anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-CTLA-4 antibody) targeting T cell co-stimulation or checkpoint pathways. 22. Patients suspected by the physician that he/she will not be compliant to the protocol conduct. 23. Pregnant women are excluded from this study; breastfeeding should be discontinued. 24. Patients participating in another clinical trial. 25. Patients not willing to sign the consent form. 26. Any psychiatric condition that would prohibit the understanding or rendering of informed consent. 27. Legal incapacity or limited legal capacity patients receiving other oncology specific medication not authorized in the protocol.