Inclusion criteria:

          -  Participant must be female >=18 years of age, able to understand the study procedures,
             and subsequently agreed to participate in the study by providing written informed
             consent.

          -  Participants must have recurrent high-grade serous, endometrioid, or clear cell
             ovarian, fallopian tube, or primary peritoneal cancer.

          -  Participants must be considered resistant to the last administered platinum therapy.

          -  Participants must have completed at least 1 but no more than 3 prior lines of therapy
             for advanced or metastatic ovarian cancer.

          -  Participants must have been previously treated with platinum-based regimen, taxane
             agent(s), and bevacizumab.

          -  Participant has measurable disease according to RECIST v.1.1.

          -  Participant has an Eastern Cooperative Oncology Group (ECOG) performance status of 0
             or 1.

          -  Participant has adequate organ function.

          -  Females with childbearing potential have a serum pregnancy test that is negative 72
             prior first dose and are not breastfeeding. Participant must also agree to abstain
             from activities that could result in pregnancy from enrollment through 180 days after
             the last dose of study treatment.

          -  Participant must provide formalin fixed paraffin embedded (FFPE) tumor tissue block(s)
             with sufficient tumor content (as confirmed by the Sponsor's designated central
             laboratory) during screening to enable BRCA testing and PD-L1 testing. Slides cut from
             FFPE blocks are not acceptable.

          -  Participant must agree to complete health-related quality of life (HRQoL)
             questionnaires throughout the study.

        Exclusion Criteria:

          -  Participant who experienced disease progression within 3 months of first-line platinum
             therapy.

          -  Participants with a known BRCA 1 or 2 mutation.

          -  Participant has received prior therapy with an anti-PD-1, anti-PD-L1 or anti-PD-L2
             agent.

          -  Participant has received prior therapy with a PARP-1/PARP-2 inhibitor.

          -  Participant has a known hypersensitivity to dostarlimab (TSR-042), Niraparib, their
             components, or their excipients.

          -  Participant has a known history of myelodysplastic syndrome or acute myeloid leukemia.

          -  Participant has not recovered from prior chemotherapy induced adverse events (AEs).

          -  Participant has a known diagnosis of immunodeficiency or is receiving systemic steroid
             therapy exceeding an equivalent of prednisone 10 mg daily or any other form of
             immunosuppressive therapy within 7 days prior to the first dose of study treatment.

          -  Participant is currently participating in a treatment study or has participated in a
             study of an investigational agent within 4 weeks of the first dose of treatment.

          -  Participant has received prior systemic anticancer therapy including cytotoxic
             chemotherapy, hormonal therapy given with the intention to treat ovarian cancer, or
             biological therapy within 3 weeks of the first dose of study treatment.

          -  Participant has received live vaccine within 14 days of planned start of study therapy

          -  Participant has symptomatic uncontrolled brain or leptomeningeal metastases. (If
             investigator feels participant symptoms are not symptomatic, participants can undergo
             a scan to confirm for eligibility).

          -  Participant had major surgery with 4 weeks of starting the study or participant has
             not recovered from any effects of any major surgery.

          -  Participant has a known additional malignancy that progressed or required active
             treatment within the last 2 years.

          -  Participant is considered a poor medical risk due to a serious, uncontrolled medical
             disorder, nonmalignant systemic disease or active controlled infection.

          -  Participant has a history or current evidence of any condition, therapy, or laboratory
             abnormality that might confound the results of the study.

          -  Participant has known active hepatitis B (hepatitis B surface antigen reactive) or
             hepatitis C (hepatitis C virus ribonucleic acid, qualitative).

          -  Participant with a known history of human immunodeficiency virus (HIV) are allowed if
             they meet all of the following criteria:

               1. Cluster of differentiation 4 >=350/μL and viral load <400 copies/milliliter (mL)

               2. No history of acquired immunodeficiency syndrome-defining opportunistic
                  infections within 12 months prior to enrollment

               3. No history of HIV-associated malignancy for the past 5 years

               4. 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 enrollment

          -  Participant is immunocompromised. Participants with splenectomy are allowed.

          -  Participant has an ongoing bowel obstruction or has other conditions that would lead
             to impaired absorption of oral niraparib.

          -  Participant has 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) is not
             considered a form of systemic treatment.