TAS-102 and Irinotecan in 2L+ Gastric and Gastroesophageal Adenocarcinoma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed gastric or gastroesophageal adenocarcinoma * Must have locally advanced, recurrent, or metastatic disease not amenable to curative intent surgery. * Must have progressed, or not tolerated, at least one line of treatment with a platinum and/or fluoropyrimidine containing regimen. At least one cycle of combination chemotherapy including a platinum (oxaliplatin, cisplatin, carboplatin) and/or fluoropyrimidine (capecitabine or 5-Fluorouracil) based regimen for advanced disease. Combination regimens with platinum/fluoropyrimidine containing a taxane and or a checkpoint inhibitor are allowed. Patients progressing within six months of perioperative chemotherapy or definitive chemoradiation for localized disease are eligible. Patients who have exhausted all other standard of care options are also eligible. * Age ≥ 18 years * Performance status: ECOG performance status ≤2 * Life expectancy of greater than 3 months * Adequate organ and marrow function as defined below: 1. leukocytes : ≥ 3,000/mcL 2. absolute neutrophil count: ≥ 1,500/mcL 3. platelets: ≥ 80,000/mcl 4. total bilirubin: within normal institutional limits 5. AST(SGOT)/ALT(SPGT): ≤ 3 X institutional upper limit of normal or ≤ 5 X if liver metastases are present 6. creatinine: \< 1.5 X upper limit of normal * The effects of TAS-102 on the developing human fetus at the recommended therapeutic dose are unknown. For this reason and because topoisomerase inhibitors are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 90 days following completion of therapy. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. 1\. A female of child-bearing potential is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: 1. Has not undergone a hysterectomy or bilateral oophorectomy; or 2. Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months). * Ability to swallow tablets * Ability to understand and the willingness to sign a written informed consent. Exclusion Criteria: * Patients who have had major surgery within 4 weeks, or chemotherapy or radiotherapy within 2 weeks prior to Cycle 1 Day 1. * All toxicities attributed to prior anti-cancer therapy other than alopecia must have resolved to grade 1 or baseline * Patients may not be receiving any other investigational agents. * Patients with known brain metastases due to poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to TAS-102, irinotecan or other agents used in study. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Prior treatment with irinotecan or TAS-102 * History of another primary cancer within the last 3 years with the exception of non-melanoma skin cancer, early-stage prostate cancer, or curatively treated cervical carcinoma in-situ. * Inability to comply with study and follow-up procedures as judged by the Investigator * Patients who are pregnant or nursing due to the potential for congenital abnormalities and the potential of this regimen to harm nursing infants.