Inclusion Criteria:  Age ≥ 18 years. ECOG performance status ≤ 1 Histologically or cytologically-confirmed TNBC (ER <1%, PR <1%, HER-2-neu 0-1+ by IHC or non-FISH-amplified63. ER-low, PR-low (defined as ER and/or PR 1-10%) and HER2-negative patients may also be eligible, as per treating MD discretion). Metastatic or recurrent TNBC. Prior progression on immune-checkpoint inhibitor and/or PDL1-negative. Note: PDL1-status may be determined on tissues from either primary or mTNBC. PD-L1 status must be determined by an FDA-approved assay approved for breast cancer, such as PharmDx IHC (22C3) for pembrolizumab, Ventana (SP142) for atezolizumab No more than 2 prior lines of systemic therapy for inoperable/recurrent or metastatic disease.  Note: Prior line of systemic therapy includes targeted or biologic agents in combination or the absence of chemotherapy  Radiation is clinically indicated for local control or palliation. At least one tumor for which RT is considered clinically appropriate. At least one radiographically-confirmed metastases index lesion that will not undergo RT and is measurable based on RECIST v1.1. Prior therapy with targeted agents or other forms of immunotherapy is allowed Prior RT is permitted, provided the treating radiation oncologist deems that study RT treatment planning guidelines can be achieved. Available archived tumor tissue of a metastatic tumor collected up to 28 days prior to registration. If archival tissue is unavailable, participant willingness 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 28 days prior to study registration.  Adequate organ function (assessed within 8 days prior to initiation of protocol treatment, unless otherwise indicated) as follows:  Hematology  Absolute Neutrophil Count (ANC) ≥1500/mm3 Platelet Count ≥100,000/mm3 Hemoglobin ≥9.0 g/dL  Renal Function  Serum Creatinine ≤ 1.5 x upper limit of normal (ULN) or Measured or calculated a creatinine clearance ≥ 60 mL/min for participant with (GFR can also be used in place of creatinine creatinine levels > 1.5 X ULN or CrCl  Hepatic Function  Total Bilirubin ≤ 1.5 mg/dL (Direct bilirubin ≤ ULN for participants with total bilirubin levels > 1.5 ULN) INR, PT, aPTT ≤ 1.5 x ULN (participants receiving anticoagulant therapy must have PT or PTT within therapeutic range) Albumin ≥ 2.5 mg/dL Aspartate Aminotransferase (AST) ≤ 2.5 x ULNb  Alanine Aminotransferase (ALT) ≤ 2.5 x ULNb ULN = upper normal limit of institution's normal range  Creatinine clearance should be calculated per institutional standard. Participants with liver metastases may have AST and/or ALT ≤ 5 x ULN Female participant has a negative urine or serum pregnancy test within 7 days prior to study treatment if a woman has child-bearing 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 non-childbearing potential.  Non-childbearing potential is defined as follows (by other than medical reasons):  ≥45 years of age and has not had menses for >1 year Patients who 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.  Women of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 180 days after the last dose of study medication. Participants of childbearing potential are those who have not been surgically sterilized or have not been free from menses for > 1 year.  Note: Abstinence is acceptable if this is the established and preferred contraception for the patient.  Male participant agrees to use an adequate method of contraception starting with the first dose of study treatment through 90 days after the last dose of study treatment. Note: Abstinence is acceptable if this is the established and preferred contraception for the patient. Male subjects must not donate sperm starting with the first dose of study drug through 90 days after the last dose of study drug. Participant must agree not to breastfeed during the study or for 30 days after the last dose of study treatment. Participant must agree to not donate blood during the study or for 90 days after the last dose of study treatment. Ability to swallow (whole) and retain oral medications. Ability to understand and the willingness to sign a written informed consent document.  Exclusion Criteria:  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) Receipt of a live vaccine within 14 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 (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed. 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.