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.