Chemotherapy and Pembrolizumab, Followed by Pembrolizumab and Olaparib As Firstline Therapy in Her-2 Negative Gastric/GEJ Adenocarcinoma

Inclusion Criteria: 1. Metastatic or unresectable, histologically confirmed Her-2 negative (as assessed locally by a certified test) adenocarcinoma of the gastroesophageal junction (AEG I- III according to Sievert´s classification) or the stomach. 2. Adjuvant/neoadjuvant or perioperative chemotherapy or chemoradiotherapy must have been finished at least 6 months before start of the study intervention. 3. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. 4. Ability for oral intake of the study drug. 5. Male/female\* participants who are at least 18 years of age on the day of signing informed consent with histologically confirmed diagnosis of esophagogastric adenocarcinoma will be enrolled in this study. * There are no data that indicate special gender distribution. Therefore, patients will be enrolled in the study gender-independently. 6. Male participants: A male participant must agree to use a contraception during the treatment period and for at least 6 months after the last dose of study intervention and refrain from donating sperm during this period. 7. Female participants: A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: 1. Not a woman of childbearing potential (WOCBP) OR 2. A WOCBP who agrees to follow the contraceptive guidance during the treatment period and for at least 6 months after the last dose of study intervention. 8. The participant provides written informed consent for the trial. 9. Have measurable or evaluable disease based on RECIST 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. 10. Have provided archival tumor tissue sample. FFPE tissue blocks are preferred to slides. 11. Have adequate organ function as defined in the following table. Specimens must be collected within 14 days prior to the start of study intervention: Hematological: * Absolute neutrophil count (ANC) ≥ 1500/µL * Platelets ≥ 100 000/µL * Hemoglobin ≥ 9.0 g/dL or ≥ 5.6 mmol/L(a) Renal: * Measured or calculated (b) creatinine clearance≥ 50 mL/min 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 prothrombin time (PT) * 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 ALT (SGPT)=alanine aminotransferase (serum glutamic pyruvic transaminase); AST (SGOT)=aspartate aminotransferase (serum glutamic oxaloacetic transaminase); GFR=glomerular filtration rate; ULN=upper limit of normal. 1. Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within the last 2 weeks. 2. Creatinine clearance (CrCl) should be calculated per institutional standard. Exclusion Criteria: 1. A WOCBP who has a positive urine pregnancy test within 72 hours prior to start of study intervention. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. 2. Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti PD L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., CTLA-4, OX 40, CD137). Has received any previous treatment with a PARP inhibitor, including Olaparib. 3. Has received prior systemic anti-cancer therapy for metastatic or locally advanced (irresectable) disease. A prior neoadjuvant or adjuvant chemotherapy is allowed (see inclusion criterion 2) 4. Persistent clinically relevant toxicities, CTCAE Grade \> 2 caused by previous cancer treatment. 5. Has received prior radiotherapy within 2 weeks of start of study intervention. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤ 2 weeks of radiotherapy) to non-CNS disease. 6. Participant received colony-stimulating factors (eg, granulocyte colony-stimulating factor \[G-CSF\], granulocyte-macrophage colony-stimulating factor \[GM CSF\] or recombinant erythropoietin) within 28 days prior to the first dose of study intervention. 7. Participant is unable to swallow orally administered medication or has a gastrointestinal disorder affecting absorption. 8. Major surgery within 2 weeks of starting study intervention and patients must have recovered from any effects of any major surgery. 9. Participant is currently receiving either strong (eg, itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate (eg. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil) inhibitors of cytochrome P450 (CYP)3A4 that cannot be discontinued for the duration of the study. The required washout period prior to starting olaparib is 2 weeks. Note: a current list of strong/moderate inhibitors of CYP3A4 can be found at the following website: https://www.fda.gov/drugs/drug-interactions-labeling/drug- development-and-drug-interactions-table-substrates-inhibitors-and-inducers 10. Participant is currently receiving either strong (phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate (eg. bosentan, efavirenz, modafinil) inducers of CYP3A4 that cannot be discontinued for the duration of the study. The required washout period prior to starting olaparib is 5 weeks for phenobarbital and 3 weeks for other agents. Note: a current list of strong/moderate inducers of CYP3A4 can be found at the following website: https://www.fda.gov/drugs/drug-interactions-labeling/drug- development-and-drug-interactions-table-substrates-inhibitors-and-inducers 11. Concomitant use of drugs inhibiting DPD activity (including sorivudine, brivudine), the required wash out phase is 4 weeks before start of the study intervention. 12. Resting ECG indicating uncontrolled, potentially reversible cardiac conditions, as judged by the investigator (e.g., unstable ischemia, uncontrolled symptomatic arrhythmia, congestive heart failure, QTcF prolongation \> 500 ms, electrolyte disturbances, etc.), or patients with congenital long QT syndrome. 13. Has received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of study drug. Administration of killed vaccines is allowed. 14. 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 intervention. 15. 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. 16. Has a known additional malignancy that is progressing or has required active treatment within the past 2 years. 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. 17. Participant has myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) or with features suggestive of MDS/AML. 18. Has known active CNS metastases and/or carcinomatous meningitis. Participants with previously completely resected brain metastases may participate if there is no sign 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 intervention. 19. Has severe hypersensitivity (≥ Grade 3) to FOLFOX or CAPOX-based chemotherapy, olaparib, pembrolizumab and/or any of its excipients. 20. Known DPD deficiency. Patients with a reduced DPD activity (CPIC activity score of 1.0-1.5) might participate in the study and receive a reduced dosage of 5- FU/capecitabine after discussion with the coordinating investigator and sponsor \[https://cpicpgx.org/guidelines/guideline-for-fluoropyrimidines-and-dpyd/\] 21. 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 (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment and is allowed. 22. Has a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. 23. Has an active infection requiring systemic therapy. 24. Has a known history of Human Immunodeficiency Virus (HIV) infection (known HIV1/HIV2 antibodies positive). 25. Has a known history of/active Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus (defined as HCV RNA is detected) infection. 26. Participant is considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, extensive interstitial bilateral lung disease on High Resolution Computed Tomography (HRCT) scan, previous allogenic bone marrow/blood transplantation or any psychiatric disorder or substance abuse that prohibits obtaining informed consent. 27. Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 6 months after the last dose of study intervention. 28. Has had an allogenic tissue/solid organ transplant.