This is a two-part, Phase II, open-label, single arm, multi-center study to determine the efficacy of pembrolizumab in combination with TAS-102 (trifluridine/tipiracil) in patients with advanced gastric cancer who have progressed after prior treatment with or without anti-PD-1/PD-L1 agent, and to further assess the safety and tolerability of this combination treatment.

This is a two-part, Phase II, open-label, single arm, multi-center study to determine the efficacy of pembrolizumab in combination with TAS-102 (trifluridine/tipiracil) in patients with advanced gastric cancer who have progressed after prior treatment with or without anti-PD-1/PD-L1 agent, and to further assess the safety and tolerability of this combination treatment. In lead-in-safety cohort, recommended dose of trifluridine/tipiracil combined with pembrolizumab will be determined with dose-limiting toxicity (DLT) and safety. Pembrolizumab dose will be fixed with current recommended dose of 400mg IV every 6 weeks (Q6W). There will be 2 dose cohort for trifluridine/tipiracil; dose level 1 is trifluridine/tipiracil 35mg/m2 BID, D1-5, D8-12, every 4 weeks (Q4W) and dose level 0 is trifluridine/tipiracil 30mg/m2 BID, D1-5, D8-12, every 4 weeks (Q4W). DLT will be evaluated during first 6 weeks. In the subsequent expansion Phase II part, patients will be recruited from four sites to evaluate the efficacy and safety of the combination therapy in 2 cohorts, anti-PD-1/PD-L1 inhibitor naive and exposure cohorts.

Inclusion Criteria:

1. Has provided written informed consent fo the trial.
2. Is male or female at least 18 years of age.
3. Has a histologically or cytologically confirmed diagnosis of advanced or metastatic gastric/gastroesophageal junction (GEJ) adenocarcinoma.
4. Has previously received at least 2 prior regiments.
5. Has a life expectancy of at least 3 months.
6. Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
7. Have 1 or more measurable disease as determined by RECIST 1.1.
8. Is able to take medications orally.
9. Has adequate organ function as defined by the following criteria.
10. Is willing to follow and follow research procedures.
11. A male participant must agree to use a contraception of this protocol during the treatment period and for at least 120 days post TAS-102.
12. A female participant is eligible to participate if she is not pregnant or breastfeeding.

Exclusion Criteria:

1. Has other concurrently active malignancies.
2. Has received prior therapy with TAS-102.
3. Is contraindicated for pembrolizumab and/or TAS-102, or have severe hypersensitivity to any of those drugs and/or their excipients.
4. Has any unresolved ≥Grade 2 toxicity (per CTCAE v5.0) attributed to any prior therapies at the time of enrollment.
5. Has had major surgery within 2 weeks prior to first dose of study interventions.
6. Has known active central nervous system (CNS) metastases.
7. Has received radiotherapy for gastric cancer treatment within 2 weeks prior to the first dose of study drugs.
8. Has received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of study drug.
9. Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug.
10. Has participated has used an investigational device within 4 weeks prior to the first dose of study intervention.
11. Has a history of uncontrollable or significant cardiovascular disease.
12. Has active (significant or uncontrolled) gastrointestinal bleeding.
13. Has active autoimmune disease that has required systemic treatment in the past 2 years.
14. Has a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease.
15. Has an active, unresolved infection requiring systemic therapy.
16. Has a known history of Human Immunodeficiency Virus (HIV) infection.
17. Has a known history of Hepatitis B (defined as Hepatitis B surface antigen [HBsAg] reactive) or known active Hepatitis C virus infection.
18. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.
19. Has had an allogenic tissue/solid organ transplant.
20. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study.