A Comparison of Platinum-based Therapy With TSR-042 and Niraparib Versus Standard of Care (SOC) Platinum-based Therapy as First-line Treatment of Stage III or IV Nonmucinous Epithelial Ovarian Cancer

Inclusion criteria: * Participants must be female, \>=18 years of age, able to understand the study procedures, and agree to participate in the study by providing written informed consent. * Participants with a histologically confirmed diagnosis of high-grade nonmucinous epithelial ovarian (serous, endometrioid, clear cell, carcinosarcoma, and mixed pathologies), fallopian tube, or peritoneal cancer that is Stage III or IV according to the International Federation of Gynecology and Obstetrics (FIGO) or tumor, node and metastasis staging criteria. * All participants with Stage IV disease are eligible. This includes those with inoperable disease, those who undergo primary debulking surgery (PDS) (R0 or macroscopic disease), or those for whom neoadjuvant chemotherapy (NACT) is planned. * Participants with Stage III are eligible if they meet protocol defined criteria. * Participants must provide a blood sample for circulating tumor deoxyribonucleic acid (ctDNA) homologous recombinant repair (HRR) testing at pre-screening or screening. * Participant must provide a minimum of 1 formalin-fixed paraffin embedded (FFPE) block slide at pre-screening or screening for PD-L1, homologous recombinant deficiency (HRD) testing. * Participants of childbearing potential must have a negative serum or urine pregnancy test (beta human chorionic gonadotropin) within 3 days prior to receiving the first dose of study treatment. * Participants must be postmenopausal, free from menses for \>1 year, surgically sterilized, or willing to use highly effective contraception to prevent pregnancy or must agree to abstain from activities that could result in pregnancy throughout the study, starting with enrollment through 180 days after the last dose of study treatment. * Participants must have adequate organ function: Absolute neutrophil count (ANC) \>=1500/micro liter (μL;) Platelet count \>=100000/μL; Hemoglobin \>=9 grams per deciliter (g/dL); Serum creatinine \<=1.5 × upper limit of normal (ULN) or calculated creatinine clearance \>=60 milliliters per minute (mL/min) using the Cockcroft-Gault equation; total bilirubin \<=1.5 × ULN or direct bilirubin \<=1.5 × ULN; AST and ALT \<=2.5 × ULN unless liver metastases are present, in which case they must be \<=5 × ULN. * Participants must have an ECOG score of 0 or 1. * Participants must have normal blood pressure (BP) or adequately treated and controlled hypertension (systolic BP \<=140 millimeters of mercury (mmHg) and/or diastolic BP \<=90 mmHg). * Participants must agree to complete health related quality of life (HRQoL) questionnaires throughout the study. * Participants must be able to take oral medication. Exclusion Criteria: * Participant has mucinous, germ cell, transitional cell, or undifferentiated tumor. * Participant has low-grade or Grade 1 epithelial ovarian cancer. * Participant has not adequately recovered from prior major surgery. * Participant is pregnant or is expecting to conceive children while receiving study drug or for up to 180 days after the last dose of study drug. Participant is breastfeeding or is expecting to breastfeed within 30 days of receiving the final dose of study drug (women should not breastfeed or store breastmilk for use, during niraparib treatment and for 30 days after receiving the final dose of study treatment). * Participant has known active central nervous system metastases, carcinomatous meningitis, or both. * Participant has clinically significant cardiovascular disease. * Participant has a bowel obstruction by clinical symptoms or computed tomography (CT) scan, subocclusive mesenteric disease, abdominal or gastrointestinal fistula, gastrointestinal perforation, or intra-abdominal abscess. * Participant has any known history or current diagnosis of myelodysplastic syndrome (MDS) or acute myeloid leukemia (AML). * Participant has been diagnosed and/or treated with any therapy for invasive cancer \<5 years from study enrollment, completed adjuvant chemotherapy and/or targeted therapy (example, trastuzumab) less than 3 years from enrollment, or completed adjuvant hormonal therapy less than 4 weeks from enrollment. * Participants with definitively treated non-invasive malignancies such as cervical carcinoma in situ, ductal carcinoma in situ, Grade 1 or 2, Stage I endometrial cancer, or non-melanomatous skin cancer are allowed. * Participant is at increased bleeding risk due to concurrent conditions (example, major injuries or major surgery within the past 28 days prior to start of study treatment and/or history of hemorrhagic stroke, transient ischemic attack, subarachnoid hemorrhage, or clinically significant hemorrhage within the past 3 months). * Participant is immunocompromised. * Participant has known active hepatitis B (example, hepatitis B surface antigen reactive) or hepatitis C (example, hepatitis C virus ribonucleic acid \[qualitative\] is detected). * Participant is considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease, or uncontrolled infection. * Participant has had investigational therapy administered within 4 weeks or within a time interval less than at least 5 half-lives of the investigational agent, whichever is longer, prior to the first scheduled day of dosing in this study. * Participant has received a live vaccine within 14 days of planned start of study therapy. Seasonal influenza vaccines that do not contain live viruses are allowed. * Participant has a known contraindication or uncontrolled hypersensitivity to the components of paclitaxel, carboplatin, niraparib, bevacizumab, dostarlimab, or their excipients. * Prior treatment for high-grade nonmucinous epithelial ovarian, fallopian tube, or peritoneal cancer (immunotherapy, anti-cancer therapy, radiation therapy). * Participant has an active autoimmune disease that has required systemic treatment in the past 2 years. Replacement therapy is not considered a form of systemic therapy (example, thyroid hormone or insulin). * Participant has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of systemic immunosuppressive therapy within 7 days prior to the first dose of study treatment.