Trial on NIraparib-TSR-042 (Dostarlimab) vs Physician's Choice CHEmotherapy in Recurrent, Ovarian, Fallopian Tube or Primary Peritoneal Cancer Patients Not Candidate for Platinum Retreatment

Inclusion Criteria: 1. Participant must have recurrent ovarian, Fallopian tube or primary peritoneal cancer not candidate for platinum retreatment; and in particular * platinum resistant patients (platinum-free interval 1-6 months from last dose of platinum) * patients for which platinum is contraindicated because of previous allergic reactions or residual toxicity (i.e nephrotoxicity or neurotoxicity) * patients not able( in physician's opinion) to receive further platinum or not willing (in patients' opinion) to receive further platinum 2. Participant must have an Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 1 3. Participants must have measurable disease or evaluable based on RECIST 1.1 (patients with only CA 125 increase without evidence of disease are not included). 4. Participant must be ≥ 18 years of age 5. Participant must have adequate organ function 6. Participant receiving corticosteroids may continue as long as their dose is stable for least 4 weeks prior to initiating protocol therapy. 7. Participant must agree to not donate blood during the study or for 90 days after the last dose of study treatment. 8. Participants must agree to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion. Newly-obtained is defined as a specimen obtained up to 6 weeks (42 days) prior to initiation of treatment on Day 1. Subjects for whom newly-obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may submit an archived specimen. 9. Female participant has a negative urine or serum pregnancy test within 7 days prior to taking study treatment if of childbearing potential and agrees to abstain from activities that could result in pregnancy from screening through 180 days after the last dose of study treatment, or is of nonchildbearing potential. 10. Participant must agree to not breastfeed during the study or for 180 days after the last dose of study treatment. 11. 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. Participants have received \>2 previous CHT lines (previous treatment with parp inhibitors and/or anti check point inhibitors is allowed providing that at least 6 months from last treatment are intercurred) 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 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 ≤ 3 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, symptomatic brain or leptomeningeal metastases 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 or any other form of immunosuppressive therapy within 7 days prior to initiating protocol therapy. 16. Participant has a known history of human immunodeficiency virus (type 1 or 2 antibodies). 17. 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). 18. 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. 19. Participant must not have a history of interstitial lung disease. 20. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. 21. Has received a live vaccine within 30 days of planned start of study therapy. Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines are live attenuated vaccines, and are not allowed.