Inclusion Criteria:

          -  Patients must have histologically or cytologically confirmed progressive metastatic or
             unresectable gastric or GEJ adenocarcinoma.

          -  Patients must have measurable disease, defined as at least one lesion that can be
             accurately measured in at least one dimension (longest diameter to be recorded for
             non-nodal lesions and short axis for nodal lesions) as >= 20 mm (>= 2 cm) by chest
             x-ray or as >= 10 mm (>= 1 cm) with computed tomography (CT) scan, magnetic resonance
             imaging (MRI), or calipers by clinical exam.

          -  Patients must have progressed after or been intolerant of at least one prior
             chemotherapy regimen. Patients with HER2 positive gastric and GEJ adenocarcinoma must
             have progressed on trastuzumab plus chemotherapy in the first line setting. Patients
             with microsatellite unstable (MSI-H) tumors must have received prior immunotherapy
             with pembrolizumab.

          -  Both men and women of all races and ethnic groups are eligible for this trial.

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 1 (Karnofsky >= 60%).

          -  Leukocytes >= 3,000/mcL.

          -  Absolute neutrophil count >= 1,500/mcL.

          -  Platelets >= 100,000/mcL.

          -  Hemoglobin >= 9 g/dL.

          -  Total bilirubin within normal institutional limits.

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (serum glutamic pyruvic transaminase [SGPT]) =< 2.5 x
             institutional upper limit of normal (ULN); if liver involvement =< 5 x ULN.

          -  Creatinine clearance >= 45 mL/min/1.73 m^2 for patients with creatinine levels above
             institutional normal.

          -  Patients must have a TP53 mutation (only those known hot-spot mutations that fall
             within exon 2 or exons 4-11 will be accepted) determined from available archived tumor
             tissue that has been subjected to next generation sequencing (NGS) through
             FoundationOne/FoundationOneCDx or a similar assay performed in a Clinical Laboratory
             Improvement Amendments (CLIA)-certified laboratory. Investigators from other sites,
             who have potential patients who meet study eligibility, will send copies of NGS
             reports from these patients via Medidata Rave case reports to the responsible study
             coordinator. Our research team will review each report to ensure each patient
             possesses the mutations of interest. Similar review will happen for each patient we
             enroll on the study at our institution. Case reports from all screened patients will
             be centrally available on the Rave study database.

          -  Nine patients must be willing to undergo endoscopic or CT guided tumor biopsies for
             mandatory correlative studies. If the biopsy is deemed not safe by the treating
             physician, the patient may still enroll given that the other eligibility criteria are
             met.

          -  The effects of M6620 on the developing human fetus are unknown. For this reason and
             because deoxyribonucleic acid (DNA)-damage response (DDR) inhibitors, as well as
             irinotecan, are known to be teratogenic, women of child-bearing potential and men able
             to father children who have female partners of child-bearing potential 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 6 months after
             trial participant's final dose of M6620 or irinotecan (whichever agent is completed
             last). Should a woman become pregnant or suspect she is pregnant while she or her
             partner is participating in this study, she should inform her treating physician
             immediately.

          -  Ability to understand and the willingness to sign a written informed consent document.

        Exclusion Criteria:

          -  Patients with early stage untreated or resectable gastric adenocarcinoma.

          -  Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for
             nitrosoureas or mitomycin C) prior to entering the study.

          -  Patients who have previously received irinotecan.

          -  Patients who have not recovered from adverse events due to prior anti-cancer therapy
             (i.e., have residual toxicities > grade 1, except alopecia) that was administered more
             than four weeks prior to starting study therapy.

          -  Patients who are receiving any other investigational agents.

          -  Patients with untreated or symptomatic brain metastases should be excluded from this
             clinical trial because of their 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 M6620 or irinotecan.

          -  M6620 is primarily metabolized by CYP3A4, and irinotecan and its active metabolite,
             SN-38, are metabolized by CYP3A4 and UGT1A1, respectively; therefore, concomitant
             administration with strong inhibitors of CYP3A4 (e.g., ketoconazole, itraconazole,
             clarithromycin, ritonavir, indinavir, nelfinavir and saquinavir) or inducers of CYP3A4
             (e.g. rifampin, phenytoin, carbamazepine, phenobarbital, St. John's Wort) should be
             avoided. Because the lists of these agents are constantly changing, it is important to
             regularly consult a frequently-updated medical reference for a list of drugs to avoid
             or minimize use of. As part of the enrollment/informed consent procedures, the patient
             will be counseled on the risk of interactions with other agents, and what to do if new
             medications need to be prescribed or if the patient is considering a new
             over-the-counter medicine or herbal product.

          -  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.

          -  Pregnant women are excluded from this study because M6620 as a DNA-damage response
             (DDR) inhibitor may have the potential for teratogenic or abortifacient effects.
             Because there is an unknown but potential risk for adverse events in nursing infants
             secondary to treatment of the mother with M6620, breastfeeding should be discontinued
             if the mother is treated with M6620. These potential risks also apply to irinotecan.

          -  Human immunodeficiency virus (HIV)-positive patients are excluded unless they have an
             undetectable viral load and are able to use anti-viral agents that do not interact
             with CYP3A4 (or regimens with agents that are not major inhibitors of cytochrome P450
             enzymes).

          -  History of other malignancy within 36 months prior to enrollment. Patients with local
             cancers of any type, provided no recurrence over this timeframe, are eligible.