Maintenance Niraparib and Dostarlimab in Advanced Cholangiocarcinoma

Inclusion Criteria: Subject must meet all of the following applicable inclusion criteria to participate in this study: * Written informed consent and HIPAA authorization for release of personal health information prior to registration. NOTE: HIPAA authorization may be included in the informed consent or obtained separately. * Age ≥ 18 years at the time of consent. * ECOG Performance Status of 0-1 within 14 days prior to registration. * Histological or cytological documentation of metastatic adenocarcinoma of the biliary tract per AJCC, 8th edition. * Measurable disease according to RECIST 1.1 within 28 days prior to registration. * Must have a defined HRD signature (BRCA1, BRCA2, PALB2, MRE, CHEK1, CHEK2, PTEN, ATM, ATR, BER, RPA1, RAD51, BARD1, BRIP1, FAAP20, FANCM, FAN1, NBN, EMSY, MRE11, ARID1A, BAP-1.) NOTE: Clinical Laboratory Improvement Act (CLIA)-certified assays including commercial tests (Foundation Medicine, Caris, Tempus, Guardant 360 or other platforms of next generation sequencing) will be allowed. * Patients must have achieved complete response (CR), partial response (PR) or stable disease (SD) after 4 to 6 months of any platinum-based therapy. * Prior treatment with immune therapy is allowed. Exception: prior treatment with PARP inhibitors is not allowed. * Prior cancer treatment must be completed at least 21 days prior to registration. Toxicities attributed to prior therapy/procedure must have resolved to Grade ≤ 1. Exceptions include alopecia and oxaliplatin induced neurotoxicity ≤ Grade 2. C1D1 treatment will start no more than 28 days after completion of prior cancer treatment. Patients that are \> 28 days from completion of prior treatment will need to be discussed with the sponsor-investigator. * Life expectancy of ≥ 16 weeks per estimation of site investigator. * Demonstrate adequate organ function as defined in the table in the protocol. All screening labs to be obtained within 7 days prior to registration. * Negative urine or serum pregnancy test done ≤ 72 hours prior to C1D1 for women of childbearing potential. * Women of childbearing potential and their partners, who are sexually active, must agree to the use contraception as described in the protocol. * Male patients must use contraception as described in the protocol. * Participants with known Hepatitis B viral infection that is controlled on nucleos(t)ide analogs (eg entecavir or tenofovir) per investigator discretion and will be continued for the duration of the study are eligible. NOTE: Risk of HBV reactivation should be considered in all patients and the need for anti-HBV prophylaxis should be carefully assessed prior to the initiation of anticancer therapy. Testing is not required at screening. Status should be assessed through medical history and if there is a question testing may be done at the discretion of the investigator based on local guidelines. This testing would be considered standard of care. * Participants who are Hepatitis C antibody positive but Hepatitis C RNA negative due to prior treatment or natural resolution of infection are eligible. Testing is not required at screening. Status should be assessed through medical history and if there is a question testing may be done at the discretion of the investigator based on local guidelines. This testing would be considered standard of care. * Participants known to be human immunodeficiency virus (HIV) serologically positive are eligible if they meet ALL of the following criteria: * Cluster of differentiation 4 ≥ 350/µL and viral load \< 400 copies/mL * No history of acquired immunodeficiency syndrome-defining opportunistic infections within 12 months prior to registration * No history of HIV associated malignancy for the past 5 years * Concurrent antiretroviral therapy as per the most current National Institutes of Health (NIH) Guidelines for the Use of Antiretroviral Agents in Adults and Adolescents Living with HIV started \> 4 weeks prior to study registration NOTE: Testing is not required at screening. Status should be assessed through medical history and if there is a question testing may be done at the discretion of the investigator based on local guidelines. This testing would be considered standard of care. * Patients must agree to not donate blood during the study or for 90 days after the last dose of study treatment. Exclusion Criteria Subjects meeting any of the criteria below may not participate in the study: * Patient is simultaneously enrolled in any interventional clinical trial. * Tumor embolization ≤ 4 weeks prior to registration. * Arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism ≤ 6 months prior to registration. * Evidence or history of bleeding diathesis or any hemorrhage or bleeding event \> CTCAE v5.0 grade 3, ≤ 4 weeks prior to registration. * Radiotherapy encompassing \> 20% of the bone marrow within 2 weeks prior to registration. Palliative radiation therapy to a small field \>1 week prior to Day 1 of study treatment may be allowed. * Major surgical procedure, open biopsy, or significant traumatic injury ≤ 28 days prior to registration AND have recovered from surgery. * Congestive heart failure - New York Heart Association (NYHA) ≥ Class II. * Uncontrolled cardiac conditions (eg. unstable ischemia, uncontrolled symptomatic arrhythmia, cardiac arrhythmias requiring anti-arrhythmic therapy, corrected QT interval by Fridericia's correction formula (QTcF) prolongation \> 500 ms, or patients with congenital long QT syndrome. NOTE: Pacemaker, beta blockers or digoxin are permitted. * Ongoing infection \> Grade 2 National Cancer Institute (NCI)-Common Terminology Criteria for Adverse Events (CTCAE) version (v)5.0. * Patient taking medications with a known risk to prolong the QTc interval and/or cause Torsades de Pointes. NOTE: Patients must be discontinued ≥ 7 days of registration. Treating physicians may wish to replace the drug(s) that do not carry this risk with safe alternative(s). * Uncontrolled hypertension. (Systolic blood pressure \> 140 mmHg or diastolic pressure \> 90 mmHg despite optimal medical management). * Seizure disorder requiring medication. * Participant has leptomeningeal disease, carcinomatous meningitis, symptomatic brain metastases, or radiologic signs of CNS hemorrhage. NOTE: Participants with asymptomatic brain metastases (i.e. off corticosteroids and anticonvulsants for at least 7 days) are permitted. * Non-healing wound, ulcer, or bone fracture. * Renal failure requiring hemo-or peritoneal dialysis. * Steroid use of \> than the equivalence of 5 mg of prednisone. * Participant must not have a history of interstitial lung disease. * Any autoimmune disease that has required systemic treatment in the past 2 years (ie, with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (eg, thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * Participant has a diagnosis of immunodeficiency or has received systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to initiating protocol therapy. * Participant has received a transfusion (platelets or red blood cells) ≤ 4 weeks prior to initiating protocol therapy. * Participant has received colony stimulating factors (e.g., granulocyte colony-stimulating factor, granulocyte macrophage colony stimulating factor, or recombinant erythropoietin) within 4 weeks prior initiating protocol therapy. * Participant has had any known Grade 3 or 4 anemia, neutropenia or thrombocytopenia due to prior chemotherapy that persisted \> 4 weeks and was related to the most recent treatment. * Known hypersensitivity to any of the study drugs, study drug classes, or excipients in the formulation. * Unable to swallow orally administered medications. * Any malabsorption condition and/or patients with gastrointestinal disorders likely to interfere with absorption of the study medication. * History of organ allograft including stem cell or cord blood transplantation. * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens. Patients considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, extensive interstitial bilateral lung disease on high resolution computed tomography (HRCT) scan or any psychiatric disorder that prohibits obtaining informed consent. * Currently receiving any other investigational agent which would be considered as a treatment for the primary neoplasm. * Participant must not have had diagnosis, detection, or treatment of another type of cancer ≤ 2 years prior to initiating protocol therapy (except basal or squamous cell carcinoma of the skin and cervical cancer that has been definitively treated). * Myelodysplastic syndrome/acute myeloid leukemia or with features suggestive of myelodysplastic syndrome/acute myeloid leukemia (MDS/AML). * Concurrent use of warfarin or other warfarin-derived anticoagulant. NOTE: Concurrent use of heparin, direct oral anticoagulants, low molecular weight heparin (LMWH), or fondaparinux is allowed. * Participant taking medications or herbal products including grapefruits, grapefruit hybrids, pomelos, star fruits, Seville oranges, pomegranates, or the juice from any of these. NOTE: Patients must discontinue the drug/product ≥ 7 days prior to registration. * Pregnant or breastfeeding (NOTE: breast milk cannot be stored for future use while the mother is being treated on study). * Judgment by the investigator that the patient should not participate in the study if the patient is unlikely to comply with study procedures, restrictions and requirements. * Substance abuse, medical, psychological or social conditions that may interfere with the patient's participation in the study or evaluation of the study results.