A Study of Pembrolizumab and Olaparib for People With Metastatic Pancreatic Ductal Adenocarcinoma and Homologous Recombination Deficiency or Exceptional Treatment Response to Platinum-Based Therapy

Inclusion Criteria: 1. This is an on-platinum maintenance trial either in a first-line or second-line setting. Participants must have either stable disease or responding disease on current first-line or second-line platinum treatment for metastatic disease. 2. Male or female patients with cytologically or histologically confirmed metastatic pancreas adenocarcinoma or acinar cell carcinoma with homologous recombination gene alterations or platinum sensitivity. Patients will be assigned to cohorts based on their genetic alterations and clinical response. Patient stratification to different Cohorts will be in the order of more canonical homologous recombination-gene (HR-gene) order. For example, patients who meet criteria for both A and B Cohorts, they will be assigned to Cohort A, not B. Cohorts will be defined as following by CLIA-approved NGS or MSK-IMPACT Part A or C: * Cohort A: Patients with either pathogenic germline or somatic alterations of 3 core HR-genes (BRCA1/2, or PALB2) who have stable or responding disease on first-line or second-line platinum therapy in two consecutive imaging assessments over at least 4 months or 16 weeks are eligible for inclusion in Cohort A. * Cohort B: Patients with either pathogenic somatic or germline non-core 15 HR-gene alterations (ATM, BAP1, BARD1, BLM, BRIP1, CHEK2, FAM175A, FANCA, FANCC, MUTYH, NBN, RAD50, RAD51, RAD51C, RTEL1) who have stable or responding disease on first-line or second-line platinum therapy in two consecutive imaging assessments over at least 4 months are eligible for inclusion in Cohort B. * Cohort C: Patients without any of the above HR-gene alterations included in Cohort A and B who have platinum-sensitivity, which is defined as a partial response (PR) or complete response (CR) for the best overall response (BOR) during at least 4 months on platinum-based therapy. Variants of unknown significance of candidate HR-genes from Cohort A or B will be eligible for Cohort C if they meet the partial response to platinum criterion. * Variants of unknown significance (VUS) or benign polymorphisms of above 17 HR-genes from Cohort A and B are considered non-pathogenic and will be excluded from cohort A or B. However, if the participant demonstrates platinum sensitivity, patient can be considered eligible for Cohort C. 3. A recurrence after curative surgery is eligible if the recurrence is \> 6 months after the last date of adjuvant therapy and the participant has at least stable or responding disease on platinum therapy and meet the above genomic or platinum sensitivity criteria. 4. Eastern Cooperative Oncology Group (ECOG) performance status 0-2 . 5. Patients must have normal organ and bone marrow function measured within 28 days prior to administration of study treatment as defined as below: * Absolute neutrophil count (ANC) ≥1500/μL * Hemoglobin ≥9.0 g/dL or ≥5.6 mmol/La * Platelets ≥100 000/μL * Total bilirubin ≤ 2 × ULN * AST (SGOT) and ALT (SGPT) ≤2.5 × ULN (≤5 × ULN for if liver metastases) * Creatinine ≤2 × ULN 6. Patients with measurable disease and/or non-measurable or no evidence of disease assessed at baseline by CT (or MRI where CT is contraindicated) are eligible. 7. Postmenopausal or evidence of non-childbearing status for women of childbearing potential: negative urine or serum pregnancy test. Postmenopausal is defined as: * Amenorrhoeic for 1 year or more following cessation of exogenous hormonal treatments * Luteinizing hormone (LH) and Follicle stimulating hormone (FSH) levels in the postmenopausal range for women under 50 * Radiation-induced oophorectomy with last menses \>1 year ago * Chemotherapy-induced menopause with \>1-year interval since last menses * Surgical sterilization (bilateral oophorectomy or hysterectomy) Exclusion Criteria: 1. Disease progression on either a first-line or the second-line platinum for metastatic PDAC or acinar cell carcinoma. 2. Patients with a second (or more) primary cancer, EXCEPTIONS: adequately treated nonmelanoma skin cancer, curatively treated in-situ cancer of the cervix, Ductal Carcinoma in Situ (DCIS), stage 1 cancers or low grade lymphomas curatively treated, without evidence of disease, and not requiring any active treatment prior to study entry are eligible 3. Resting EKG with QTC ≥ 450 msec detected on 2 or more time points within a 24-hour period or family history of long QT syndrome. If EKG demonstrates QTC ≥ 450 msec, patient will only be eligible if repeat EKG demonstrates QTC ≤ 450 msec. 4. Patients with myelodysplastic syndrome/acute myeloid leukaemia or with features suggestive of MDS/AML. 5. Previous allogeneic bone marrow transplant. 6. Patients with symptomatic uncontrolled brain metastases. A scan to confirm the absence of brain metastases is not required for eligibility. The patient can receive a stable dose of corticosteroids before and during the study as long as the steroids were started at least 4 weeks prior to treatment and the steroid dose is \< 10 mg/day. Patients with spinal cord compression unless considered to have received definitive treatment for this and evidence of clinically stable disease for 28 days. 7. Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the study medication. 8. 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. 9. Immunocompromised patients, e.g., patients who are known to be serologically positive for human immunodeficiency virus (HIV). 10. Patients with known active hepatitis (i.e. Hepatitis B or C). 1. Active hepatitis B virus (HBV) is defined by a known positive HBV surface antigen (HBsAg) result. Patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody and absence of HBsAg) are eligible. 2. Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA. 3. Has a known history of active TB (Bacillus tuberculosis). 11. Any prior treatment with any PARP inhibitor, including olaparib. 12. Any previous treatment with any anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. 13. Has received systemic therapy 2 weeks prior to starting treatment 14. Patients with any recent investigational agents are not eligible unless at least 2 weeks or 5 half-lives of investigational agent prior to the first dose of study treatment have passed. 15. Live vaccines within 30 days prior to the first dose of study treatment and while participating in the study are not permitted. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster, yellow fever, rabies, BCG, and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist®) are live attenuated vaccines and are not allowed. 16. Active autoimmune disease that has required systemic treatment in the past 2 years is not permitted (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. 17. Palliative radiotherapy must have been completed 14 or more days before Cycle 1 Day 1. 18. If participant received major surgery within 4 weeks before screening, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. 19. Participants must have recovered from all AEs due to previous therapies to ≤Grade 1 or baseline. Participants with ≤Grade 2 neuropathy may be eligible. Participants with ≤Grade 2 alopecia may be eligible as well. 20. Concomitant use of known strong CYP3A inhibitors (e.g. itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate CYP3A inhibitors (e.g. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil). The required washout period prior to starting is 2 weeks. 21. Concomitant use of known strong (e.g. phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate CYP3A inducers (e.g. bosentan, efavirenz, modafinil). The required washout period prior to starting is 5 weeks for enzalutamide or phenobarbital and 3 weeks for other agents.