Participants who meet any of the following criteria will be excluded:
* Known germline or somatic BRCA mutation-positive status
* Known active brain metastases or LMD (leptomeningeal disease). Note: Patients with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging [using the identical imaging modality for each assessment, either MRI or CT scan] for at least 4 weeks prior to the first dose of study treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and have not been using steroids for at least 7 days prior to study treatment.
* Known additional malignancy that progressed or required treatment in the last 2 years. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer.
* Prior treatment with either a PARP inhibitor or ICI is permitted, however, prior receipt of both therapies is excluded
* Receipt of >2 lines of chemo in the metastatic setting (including targeted or biologic agents in combination or the absence of chemotherapy)
* Hypersensitivity to niraparib or dostarlimab components or its excipients.
* Participation in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks (or at least 5 half-lives from previous therapy) of the first dose of study treatment.
* Receipt of prior cytotoxic therapy or targeted small molecule therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., > Grade 1 or at baseline) from adverse events due to a previously administered agent, including grade 2 alopecia.
Note: Participants with ≤ Grade 2 neuropathy are an exception to this criterion and may qualify for the study.
* Patients who have undergone any major surgery within 3 weeks prior to study entry: patients must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy.
* Active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment.
* Diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. Use of local corticosteroid injections (e.g. intra-articular injections), inhaled, intranasal, ophthalmic, and topical corticosteroids, and subjects requiring corticosteroid pre-medication for hypersensitivity reactions (e.g. CT scan pre-medication) are allowed.
* Known history of/active, non-infectious pneumonitis requiring treatment with steroids or has history of/active interstitial lung disease.
* Active infection requiring systemic therapy.
* History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the patient's participation for the full duration of the trial, or is not in the best interest of the patient to participate, in the opinion of the treating investigator.
* Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.
* Participant has 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.
Pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 180 days after the last dose of trial treatment.
* Known history of myelodysplastic syndrome (MDS) or acute myeloid leukemia (AML).
* Known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies).
* Known active Hepatitis B (e.g., HbsAg reactive) or Hepatitis C (e.g., HCV RNA [qualitative] is detected).
* Known history of active TB (Bacillus Tuberculosis)
* Participant must not have received a transfusion (platelets or red blood cells) ≤ 4 weeks prior to initiating protocol therapy.
* 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.
* 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.
* Patient experienced ≥ Grade 3 immune-related AE with prior immunotherapy, with the exception of non-clinically significant lab abnormalities.