Inclusion Criteria:

          1. Metastatic, recurrent, or unresectable solid tumor with a pathogenic, or presumed
             pathogenic, somatic mutation of one of the following homologous recombination
             deficiency (HRD) gene mutations:

             • BRCA1, BRCA2, ATM, RAD51B, RAD51C, RAD54L, RAD51D, FANC/BRIP1, FANCI, FANCL,
             FANCN(PALB2), BARD1, CHEK1, CHEK2, CDK12, or PPP2R2A.

          2. Participant must have an Eastern Cooperative Oncology Group (ECOG) performance status
             of ≤ 1

          3. Participant must be ≥ 18 years of age

          4. Participant must have adequate organ function, defined as follows:

               -  Absolute neutrophil count ≥ 1,500/µL

               -  Platelets ≥ 100,000/µL

               -  Hemoglobin ≥ 9 g/dL

               -  Serum creatinine ≤ 1.5 x upper limit of normal (ULN) or calculated creatinine
                  clearance ≥ 60mL/min using the Cockcroft-Gault equation

               -  Total bilirubin ≤ 1.5 x ULN (≤2.0 in patients with known Gilberts syndrome) OR
                  direct bilirubin ≤ 1 x ULN

               -  Aspartate aminotransferase and alanine aminotransferase ≤ 2.5 x ULN unless liver
                  metastases are present, in which case they must be ≤ 5 x ULN

               -  International normalized ratio (INR) or prothrombin time (PT) ≤1.5× ULN unless
                  patient is receiving anticoagulant therapy as long as PT or partial
                  thromboplastin (PTT) is within therapeutic range of intended use of
                  anticoagulants. Activated partial thromboplastin time (aPTT) ≤1.5× ULN unless
                  patient is receiving anticoagulant therapy as long as PT or PTT is within
                  therapeutic range of intended use of anticoagulants

          5. Participant must agree to not donate blood during the study or for 90 days after the
             last dose of study treatment.

          6. Female participant has a negative serum pregnancy test within 72 hours prior to taking
             study treatment if of childbearing potential and agrees to use a highly effective
             method of contraception from screening through 180 days after the last dose of study
             treatment, or is of non-childbearing potential. Non-childbearing potential is defined
             as follows (by other than medical reasons):

               -  ≥45 years of age and has not had menses for >1 year

               -  Patients who have been amenorrhoeic for <2 years without history of a
                  hysterectomy and oophorectomy must have a follicle stimulating hormone value in
                  the postmenopausal range upon screening evaluation

               -  Post-hysterectomy, post-bilateral oophorectomy, or post-tubal ligation.
                  Documented hysterectomy or oophorectomy must be confirmed with medical records of
                  the actual procedure or confirmed by an ultrasound. Tubal ligation must be
                  confirmed with medical records of the actual procedure, otherwise the patient
                  must be willing to use an adequate barrier method throughout the study, starting
                  with the screening visit through 180 days after the last dose of study treatment.
                  See Section 5.4 for a list of acceptable birth control methods. Information must
                  be captured appropriately within the site's source documents. Note: Abstinence is
                  acceptable if this is the established and preferred contraception for the
                  patient.

        h. Male participant agrees to use a highly effective method of contraception (see Section
        5.4 for a list of acceptable birth control methods) starting with the first dose of study
        treatment through 180 days after the last dose of study treatment. Note: Abstinence is
        acceptable if this is the established and preferred contraception for the patient.

        i. Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral
        therapy with documented undetectable viral load and CD 4 count of >350 within 6 months of
        the first dose of study treatment are eligible for this trial.

        j. If an appropriate archival tumor tissue sample is not available, patient is willing to
        undergo a pre-treatment tumor biopsy.

        k. Participant must be able to understand the study procedures and agree to participate in
        the study by providing written informed consent

        Exclusion Criteria:

          1. Participant must not be simultaneously enrolled in any interventional clinical trial

          2. Patients with the following malignancies will be excluded:

               -  Prostate cancer

               -  Ovarian, breast, and pancreatic patients with known germline BRCA1 or BRCA2
                  mutation

               -  Platinum sensitive ovarian cancer (defined as recurrence > 6 months from last
                  platinum agent), unless platinum intolerant.

          3. Participant must not have had major surgery ≤ 3 weeks prior to initiating protocol
             therapy and participant must have recovered from any surgical effects.

          4. Participant must not have received investigational therapy ≤ 4 weeks, or within a time
             interval less than at least 5 half-lives of the investigational agent, whichever is
             shorter, prior to initiating protocol therapy.

          5. Participant has had radiation therapy encompassing >20% of the bone marrow within 2
             weeks; or any radiation therapy within 1 week prior to Day 1 of protocol therapy.

          6. Participant must not have a known hypersensitivity to niraparib and dostarlimab
             components or excipients.

          7. Participant must not have received a transfusion (platelets or red blood cells) ≤ 4
             weeks prior to initiating protocol therapy.

          8. Participant must not have received colony stimulating factors (eg, granulocyte
             colony-stimulating factor, granulocyte macrophage colony stimulating factor, or
             recombinant erythropoietin) within 4 weeks prior initiating protocol therapy.

          9. 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.

         10. Participant must not have any known history of myelodysplastic syndrome (MDS) or acute
             myeloid leukemia (AML)

         11. Participant must not have a serious, uncontrolled medical disorder, nonmalignant
             systemic disease, or active, uncontrolled infection. Examples include, but are not
             limited to, uncontrolled ventricular arrhythmia, recent (within 90 days) myocardial
             infarction, uncontrolled major seizure disorder, unstable spinal cord compression,
             superior vena cava syndrome, or any psychiatric disorder that prohibits obtaining
             informed consent

         12. 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)

         13. Participant must not have known leptomeningeal disease, carcinomatous meningitis,
             symptomatic brain metastases, or radiologic signs of CNS hemorrhage.

             • Patients with a history of brain metastases may be enrolled if the metastases are
             fully treated with either resection or irradiation, the patient is asymptomatic for 4
             weeks, and the patient is off steroids.

         14. Patient experienced ≥ Grade 3 immune-related AE with prior immunotherapy, with the
             exception of non-clinically significant lab abnormalities.

         15. Participant has a diagnosis of immunodeficiency or has received systemic steroid
             therapy at a dose of >10 prednisone or its equivalent or any other form of
             immunosuppressive therapy within 7 days prior to initiating protocol therapy.

         16. Participant has known active hepatitis B (e.g., hepatitis B surface antigen [HBsAg]
             reactive) or hepatitis C (e.g., hepatitis C virus [HCV] ribonucleic acid [qualitative]
             is detected).

         17. Participant has an active 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.

         18. Participant must not have a history of interstitial lung disease.

         19. Participant has received a live vaccine within 14 days of initiating protocol therapy.