Selinexor in Combination With Irinotecan in Adenocarcinoma of Stomach and Distal Esophagus

Inclusion Criteria: * Must have histologically confirmed gastric, gastro-esophageal junction or distal esophageal adenocarcinoma (predominant histology) that is recurrent, metastatic or unresectable * Must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) criteria 1.1 * Must have received at least one line but less than three lines of prior systemic therapies and have either progressed or intolerant to prior therapies. Patients who have received adjuvant/neoadjuvant therapy within last one year will be eligible as well. * Eastern Cooperative Oncology Group (ECOG) performance status ≤1 * Life expectancy of greater than 3 months * Must have normal organ and marrow function * Women of child-bearing potential (WOCBP) must agree to use dual methods of contraception and have a negative serum pregnancy test at screening. Male participants must use an effective barrier method of contraception if sexually active with a WOCBP. For both male and female participants, effective methods of contraception must be used throughout the study and for three months following the last dose. * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Have had chemotherapy, biologic therapy or radiotherapy within 3 weeks prior to entering the study * Are receiving any other investigational agents for anti-cancer treatment within 3 weeks of starting study medication * Symptomatic central nervous system (CNS) metastases * Progression on irinotecan containing regimen * History of allergic reactions attributed to compounds of similar chemical or biologic composition to irinotecan * Major surgery within 2 weeks before cycle 1 Day 1 (C1D1) * Unstable cardiovascular function * Patients who are pregnant or lactating * Uncontrolled infection requiring parenteral antibiotics, antivirals, or antifungals within one week prior to first dose; patients with controlled infection or on prophylactic antibiotics are permitted in the study. * Known active hepatitis A, B, or C infection; or known to be positive for HCV RNA or HBsAg (HBV surface antigen) * Any underlying condition that would significantly interfere with the absorption of an oral medication * \> Grade 2 peripheral neuropathy at baseline * Serious psychiatric or medical conditions that could interfere with treatment * Concurrent therapy with approved or investigational anticancer therapeutic other than steroids * History of gastrointestinal perforation and/or fistulae within 6 months prior to C1D1 * Use of strong CYP3A4 inducers or inhibitors within 2 weeks of starting study medication