Phase II Trial of the PARP Inhibitor Niraparib and PD-1 Inhibitor Dostarlimab in Patients With Advanced Cancers With Active Progressing Brain Metastases (STARLET)

Inclusion Criteria: 1\. Age ≥ 18 years old. 2. Participant must have brain metastasis and either 1\. Advanced BRCA1/2m cancer 2. Advanced HRR-aberrant, non-BRCA1/2m cancer 3. Advanced small cell lung cancer 4. Advanced non-small cell lung cancer 5. Advanced Triple Negative Breast Cancer 3. In cohorts 1 and 2, subjects will be eligible for this study based on the presence of actionable aberrations in one or more of the following HRR genes: BRCA1/2, ATM; BRIP1; CDK12; CHEK1; CHEK2; FANCL; PALB2; RAD51; RAD51B; RAD51C; RAD51D; RAD52; RAD54L, or other related genes at the discretion of the principal investigator in consultation with the MD Anderson Cancer Center Institute for Personalized Cancer Therapy Precision Oncology Decision Support (PODS) group. Variant interpretation for actionability will be performed by PODS. 4\. Any prior SRS to brain lesions or prior excision must have occurred ≥1 week before the start of dosing for this study. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. 5\. Patients must have had at least one prior line of systemic therapy directed at their malignancy. 6\. Participant must have an Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2. 7\. Adequate organ function as described below: (Note: CBC test should be obtained without transfusion or receipt of colony-stimulating factors in the 2 weeks before obtaining). Hematological • Absolute neutrophil count (ANC) ≥1,500 /mcL • Platelets ≥ 100,000 / mcL • Hemoglobin ≥ 9.0 g/dL • Serum creatinine ≤1.5xULN OR Measured or calculated creatinine clearance ≥50 mL/min for participants. Hepatic * Serum total bilirubin ≤1.5xULN OR Direct bilirubin ≤1 x ULN for subjects with total bilirubin levels ≥1.5xULN ) (if associated with liver metastases or Gilbert's disease, ≤2.5 x ULN) * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤2.5 x ULN (if associated with liver metastases, ≤5 x ULN) Coagulation * International Normalized Ratio (INR) or Prothrombin Time (PT) and Activated Partial Thromboplastin Time (aPTT) ≤1.5xULN, unless subject is receiving anticoagulant therapy. 8\. Participant must have at least one measurable brain metastasis (tumor diameter of 0.5-3 cm by mRECIST on magnetic resonance imaging \[MRI\]) for which all of the following criteria have to be met: asymptomatic (no neurologic signs or symptoms), unirradiated, not requiring immediate local intervention (surgery or radiosurgery), and not requiring systemic glucocorticoid therapy within 10 days prior to study treatment initiation. Patient may have other metastatic lesions which can have had irradiation. 9\. Patients must have archival systemic tumor tissue available at screening. Patients who do not have tissue specimens available may undergo a biopsy during the screening period. Acceptable samples include core-needle biopsies for deep systemic tumor tissue or excisional, incisional, punch, or forceps biopsies for cutaneous, subcutaneous, or mucosal lesions. Representative formalin-fixed paraffin-embedded (FFPE) tumor specimens in paraffin blocks (blocks are preferred) OR at least 4 unstained slides, with an associated pathology report, for testing of tumor PD-L1 expression. Tumor tissue should be of good quality based on total and viable tumor content. 10\. Female participant has a negative serum pregnancy test within 3 days prior to taking study treatment if of childbearing potential and agrees use a highly effective method of contraception (\< 1% failure rate with low user dependency) from screening through 180 days after the last dose of study treatment or is of nonchildbearing potential. Nonchildbearing potential is defined as follows (by other than medical reasons): * Patients who are ≥45 years of age and who have not had menses for \>1 year or have been amenorrhoeic for \<2 years without history of a hysterectomy and oophorectomy must have a follicle stimulating hormone value in the postmenopausal range upon screening evaluation * Post-hysterectomy, post-bilateral oophorectomy, or post-tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure, otherwise the patient must be willing to use an adequate barrier method throughout the study, starting with the screening visit through 180 days after the last dose of study treatment. See Section 4.4 for a list of acceptable birth control methods. Information must be captured appropriately within the site's source documents. Note: Abstinence is acceptable if this is the established and preferred contraception for the patient. * Participant must agree to not breastfeed during the study or for 180 days after the last dose of study treatment. 11\. Male participants are eligible to participate if they agree to the following during the treatment period and for at least 180 days after the last dose of study treatment: * Refrain from donating sperm plus, either: * Be abstinent from sexual activity as their preferred and usual lifestyle (abstinent on a long-term and persistent basis) and agree to remain abstinent or * Must agree to use a male condom (and should also be advised of the benefit for a female partner to use a highly effective method of contraception as a condom may break or leak) 12. Participant must have signed and dated an IRB/IEC approved written informed consent form in accordance with regulatory and institutional guidelines. This must be obtained before the performance of any protocol related procedures that are not part of normal subject care. Hence, participants must have the ability to understand and the willingness to sign the approved written informed consent document. 13\. Participant must be willing and able to comply with scheduled visits, treatment schedule, laboratory testing, and other requirements of the study. Exclusion Criteria: 1. Participant must not be simultaneously receiving interventional anticancer treatment. 2. Participant must not have contraindications to MRI (implanted metal device or foreign bodies) or MRI contrast (insufficient renal function or allergy). 3. A history of / or suffers from claustrophobia or subject feels unable to lie flat and still on their back for the required period of time in an MRI or PET/CT scanner. 4. Participant must not have symptomatic or untreated spinal cord compression. 5. Participant must not have evidence of leptomeningeal disease. 6. Participant must not have previously received a combination of PARP inhibitor and PD-1/L1inhibitor. Participant must not have previously received equivalent of full dose single agent PARPi. Prior therapy with PD-1/L1-inhibitor is permitted. 7. For participants choosing optional CSF collection via lumbar puncture: no medical contraindication to lumbar puncture may be present (including severe coagulopathy, radiographic concern for impending herniation or obstructive hydrocephalus, or soft tissue infection at puncture site, as outlined in MD Anderson institutional policy). LP may be deferred if at any time the treating physician determines that it would be unsafe to perform this procedure due to the characteristics of the brain metastases (eg. size, associated edema, etc). 8. Participant must not have had major surgery ≤ 3 weeks prior to initiating protocol therapy and participant must have recovered from any surgical effects. 9. Participant must not have received systemic anticancer therapy ≤2 weeks prior to initiating protocol therapy. 10. Previous systemic radiation therapy encompassing \>20% of the bone marrow (but not encompassing the CNS) within 2 weeks 11. Previous stereotactic or highly conformal radiotherapy within 1 week before the start of dosing for this study, whole brain radiotherapy within 2 weeks. 12. Participant must not have a known hypersensitivity to niraparib and dostarlimab components or excipients. 13. Participants with an inactive, known or suspected autoimmune disease. Subjects with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll. 14. Participant must not have a history of interstitial lung disease. 15. Participants with a major medical, neurologic or psychiatric condition who are judged as unable to fully comply with study therapy or assessments should not be enrolled. 16. Participant has a history of a second malignancy, unless potentially curative treatment has been completed with no evidence of malignancy for 2 years. 17. Patients with prostate cancer are excluded from this trial. 18. Participant has a known history of active hepatitis B or hepatitis C. Prior treated hepatitis B or C with undetectable viral load may be enrolled. 19. Participants who have a known history of HIV positive and are on effective anti-retroviral therapy with documented undetectable viral load and CD4 count ≥350 within 6 months of the first dose of study treatment are eligible. 20. Participants unable to undergo contrast enhanced brain MRI. 21. Participants unable to swallow pills or have significant gastrointestinal disease which would preclude the adequate oral absorption of medications. 22. Patients who have received live vaccines within 30 days of study entrance. 23. Patients with uncontrolled high blood pressure (HTN \>140/90). 24. Patients with prior diagnosis of MDS or AML.