Study of SBRT/Olaparib Followed by Pembrolizumab/Olaparib in Gastric Cancers

Inclusion Criteria: 1. Provision to sign and date the consent form. 2. Participant must be ≥ 18 years of age 3. Histologically confirmed metastatic gastric or GEJ adenocarcinoma that is amenable to biopsy either at primary or metastatic site. 4. Patient must consent at initiation of study to serial tumor biopsies during study. Irradiated lesions will not be considered for biopsy. For baseline biopsy, available archived tumor tissue of a metastatic tumor collected up to 28 days prior to registration is acceptable. If, after patient consent, the tumor is deemed inaccessible, the biopsy is not in the subject's best interest per investigator discretion, or the patient refuses biopsy during course of the study, patients will be allowed to remain on study. 5. Participant must have a primary tumor or a single metastatic site amenable to radiation in: the stomach, esophagus, liver, lungs, pancreas, thoracic/abdominal LNs, or soft tissues. Of note - sites of disease planned to be biopsied should not be radiated. 6. Participant must have at least one radiographically-confirmed index lesion that will not undergo RT and is measurable based on RECIST v1.1. 7. Homologous recombination deficiency cohort: pre-identified presence of somatic or germline deleterious mutation, as determined by NGS only, in at least one gene critical to DNA repair through homologous recombination, including but not limited to: ARID1A, ATM, ATRX, MRE11A, NBN, PTEN, RAD50/51/51B, BARD1, BLM, BRCA1, BRCA2, BRIP1, FANCA/C/D2/E/F/G/L, PALB2, WRN, CHEK2, CHEK1, BAP1, FAM175A, SLX4, MLL2 or XRCC. 1. All patients must undergo NGS testing in a CLIA certified, CAP tested and bioinformatics-validated testing lab PRIOR to protocol treatment, to determine which cohort they are eligible for - HRD versus HR proficient. The testing may have been done at any time prior to enrollment. 2. For patients within whom a deleterious mutation in the homologous recombination pathway is found, the determination of a deleterious mutation must be supported in the documentation included in the testing, and should include clinical, or pre-clinical literature to support the finding that a specific mutation results in impaired function of the gene, and thus impaired DNA repair through homologous recombination. Variants of unknown significance will not be eligible. 3. Patients with germline deleterious mutations may have been identified at any time point prior to inclusion in the protocol and do NOT need to have this genetic testing repeated regardless of time frame and intervening therapy. 8. Participants must have received at least one line of therapy including a fluoropyrimidine and platinum drug. For participants with HER2+ tumors, they must have received trastuzumab. Adjuvant therapy does not count toward first-line therapy unless patient recurs within 6 months of completion. 9. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. 10. Participants must have the ability to swallow whole pills and liquids at the Screening Visit and, in the investigator's judgement, for the duration of the study. 11. Have adequate organ function as defined in Table 1: Table 1: Adequate Organ Function Laboratory Values: System: Laboratory Value: Hematological Absolute neutrophil count (ANC) ≥1500/μL Platelets ≥100 000/μL Hemoglobin ≥9.0 g/dL or ≥5.6 mmol/La Renal Creatinine OR Measured or calculated creatinine ≤1.5 × ULN OR ≥30 mL/min for participant with creatinine levels \>1.5 × institutional ULN clearance (GFR can also be used in place of creatinine or CrCl) Hepatic Total bilirubin ≤1.5 ×ULN OR direct bilirubin ≤ULN for participants with total bilirubin levels \>1.5 × ULN AST (SGOT) and ALT (SGPT) ≤2.5 × ULN (≤5 × ULN for participants with liver metastases) Coagulation International normalized ratio (INR) OR ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of prothrombin time (PT) intended use of anticoagulants Activated partial thromboplastin time (aPTT) ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants 12. Participant receiving corticosteroids, for reasons other than radiation related toxicities, may continue as long as their dose is stable (meaning no increase or on tapering dose) for least 4 weeks prior to initiating protocol therapy. 13. Female participants are eligible if they are: not pregnant (within 28 days prior to start of study treatment - see Appendix 3), not breastfeeding, and at least one of the following conditions applies: a.) Not a woman of childbearing potential (WOCBP) as defined in Appendix 3 OR b.) A WOCBP who agrees to follow contraceptive guidance during the treatment period and for at least 120 days after the last dose of study treatment. 14. Male participants must agree to use a contraception as detailed in Appendix 3 of this protocol during the treatment period and for at least 120 days after the last dose of study treatment and refrain from donating sperm during this period. Exclusion Criteria: An individual who meets any of the following criteria will be excluded from participation in this study: 1. Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks prior to allocation. 1. Note: Participants must have recovered from all AEs due to previous therapies to ≤Grade 1 or baseline. Participants with ≤Grade 2 neuropathy may be eligible. 2. Note: If participant received major surgery within 4 weeks, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. 2. Has received prior radiotherapy within 2 weeks of start of study treatment. Participants must have recovered from all radiation-related toxicities, not require corticosteroids specifically for radiation toxicities, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤2 weeks of radiotherapy) to non-CNS disease. 3. Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist®) are live attenuated vaccines and are not allowed. Note: Vaccines for SARS CoV- 2 will be permitted before and during the course of study. 4. Is currently participating in, or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study treatment. Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent. 5. Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. 6. Has a known additional malignancy that is progressing or has required active treatment within the past 3 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g. breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded 7. Has known active CNS metastases and/or carcinomatous meningitis that requires ongoing treatment or are found to be progressing. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study treatment. 8. Has severe hypersensitivity (≥Grade 3) to pembrolizumab or olaparib and/or any of its excipients. 9. Participant must not have impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of the study drugs (e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection). 10. Has 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 (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. 11. Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. 12. Has an active infection requiring systemic therapy. 13. Has a known history of Human Immunodeficiency Virus (HIV).