• 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, an mixed pathologies), fallopian tube, or primary 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); (complete cytoreduction [CC0] or macroscopic disease), or those for whom neoadjuvant chemotherapy (NACT) is planned.
• Participants with Stage III are eligible if they meet one or more of the following criteria:
  • Stage IIIC participants with CC0 resection if they meet the following criteria: Aggregate >=5 cm extra-pelvic disease during PDS as assessed by the investigator
  • All participants with inoperable Stage III disease.
  • All Stage III participants with macroscopic residual tumor (per investigator judgement) following PDS.
  • All Stage III participants for whom NACT is planned.
• 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 formalin-fixed paraffin embedded (FFPE) block 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 Eastern Cooperative Oncology Group (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.

• Participant has mucinous, germ cell, transitional cell, or undifferentiated tumor.
• Participant has low-grade or Grade 1 epithelial ovarian cancer.
• Stage III participant with R0 resection after PDS (i.e., no macroscopic residual disease, unless the participant has aggregate 5cm extra-pelvic disease during primary debulking surgery.
• Participant has not adequately recovered from prior major surgery.
• Participant has a known condition, therapy, or laboratory abnormality that might confound the study results or interfere with the participant’s participation for the full duration of the study treatment in the opinion of the investigator.
• 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 (example, significant cardiac conduction abnormalities, uncontrolled hypertension, myocardial infarction, uncontrolled cardiac arrhythmia or unstable angina <6 months to enrollment, New York Heart Association Grade 2 or greater congestive heart failure, serious cardiac arrhythmia requiring medication, Grade 2 or greater peripheral vascular disease, and history of cerebrovascular accident within 6 months).
• 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 initiating bevacizumab as SOC has proteinuria as demonstrated by urine protein:creatinine ratio >=1.0 at Screening or urine dipstick for proteinuria >=2 (participants discovered to have >=2 proteinuria on dipstick at baseline should undergo a 24-hour urine collection and must demonstrate <2 grams (g) of protein in 24 hours to be eligible).
• 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 IA 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. Participants with splenectomy are allowed. Participants with well-controlled known HIV are allowed 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 enrolment; No history of HIV-associated malignancy for the past 5 years; Concurrent anti-retroviral therapy as per the most current National Institutes of Health (NIH) Guidelines for the Use of Anti-retroviral Agents in Adults and Adolescents Living with HIV started >4 weeks prior to study enrolment.
• 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 active, uncontrolled infection. Specific examples include, but are not limited to, history of non-infectious pneumonitis that required steroids, current pneumonitis, uncontrolled autoimmune disease, uncontrolled ventricular arrhythmia, recent myocardial infarction within 90 days of consent, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, or any psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the study (including obtaining informed consent).
• 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.

Regimen consisting of platinum-based combination chemotherapy standard-of-care (SOC) combined with the anti-PD-1, dostarlimab, followed by dostarlimab plus niraparib-based maintenance therapy compared to SOC platinum-based combination therapy in patients with newly diagnosed Stage III or IV nonmucinous epithelial cancer of the ovary, fallopian tube, or primary peritoneum

• Patients will be provided a travel stipend
• Research Medications and treatment are provided at no charge.
• Medication, treatment, and testing considered standard of care will be billed to the patient’s insurance carrier

Participants will receive SOC during the chemotherapy Run-In period (cycle 1) before randomization to study treatment (cycle 2).