Pembrolizumab is a potent humanized immunoglobulin G4 (IgG4) monoclonal antibody (mAb) with high specificity of binding to the programmed cell death 1 (PD 1) receptor, thus inhibiting its interaction with programmed cell death ligand 1 (PD-L1) and programmed cell death ligand 2 (PD-L2). Olaparib is a potent PARP inhibitor (PARP1, 2, and 3) that is being developed as a monotherapy as well as for combination with chemotherapy, ionizing radiation, and other anti-cancer agents including novel agents and immunotherapy. Paclitaxel is widely used in breast, lung and gastric cancer with every 3-week or weekly cycle. Various targeted anticancer agents have been investigated with paclitaxel and combination with ramucirumab, a monoclonal anti-VEGFR2 antibody, was approved as a 2nd line treatment.

Pembrolizumab is a potent humanized immunoglobulin G4 (IgG4) monoclonal antibody (mAb) with high specificity of binding to the programmed cell death 1 (PD 1) receptor, thus inhibiting its interaction with programmed cell death ligand 1 (PD-L1) and programmed cell death ligand 2 (PD-L2). Olaparib is a potent PARP inhibitor (PARP1, 2, and 3) that is being developed as a monotherapy as well as for combination with chemotherapy, ionizing radiation, and other anti-cancer agents including novel agents and immunotherapy. Paclitaxel is widely used in breast, lung and gastric cancer with every 3-week or weekly cycle. Various targeted anticancer agents have been investigated with paclitaxel and combination with ramucirumab, a monoclonal anti-VEGFR2 antibody, was approved as a 2nd line treatment.

Inclusion Criteria:

1. Provided written informed consent for treatment.
2. Age ≥ 19 years old
3. measurable or evaluable disease based on RECIST 1.1. Lesions
4. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 on time of patient's allocation.
5. Adequate organ function as defined by the following criteria:
6. A life expectancy of at least 3 months
7. Is able to swallow and retain orally administered medications
8. Failed first-line trastuzumab treatment for HER2 positive patients
9. Highly effective contraception for both male and female subjects if the risk of conception exists.
10. Left ventricular ejection fraction (LVEF) ≥50%

Exclusion Criteria:

1. A WOCBP who has a positive urine pregnancy test within 72 hours prior to allocation
2. Has received prior systemic anti-cancer therapy including investigational agents within 2 weeks prior to allocation.
3. Has received prior radiotherapy within 2 weeks of start of study treatment.
4. Has received a live vaccine within 30 days prior to the first dose of study drug.
5. Is currently participating in or has participated in a study of an investigational agent including trastuzumab or has used an investigational device within 4 weeks prior to the first dose of study treatment.
6. 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.
7. Has a known additional malignancy that is progressing or has required active treatment within the past 5 years.
8. Has known active CNS metastases and/or carcinomatous meningitis.
9. Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients, PARP inhibitor and paclitaxel.
10. Has active autoimmune disease that has required systemic treatment in the past 2 years
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).
14. Has an active of Hepatitis B (defined as Hepatitis B surface antigen [HBsAg] reactive and HBV titer >2000 IU/ml) or known active Hepatitis C virus (defined as HCV RNA is detected) infection.
15. Has an active TB (Bacillus Tuberculosis) with treatment.
16. Participant has received previous allogenic bone-marrow, tissue/solid organ transplant or double umbilical cord transplantation (dUCBT).