The purpose of the study is to test the effects, both good and bad, of the research study drug Neratinib in combination with Trastuzumab, Pembrolizumab and FOLFOX chemotherapy. This study will also look at the safety of Neratinib in combination with Trastuzumab, Pembrolizumab and FOLFOX in HER2 overexpressing Gastroesophageal cancers.

Inclusion Criteria:

• Patients must have pathologically or cytologically confirmed esophageal, gastric or gastroesophageal junction (GEJ) adenocarcinoma by the enrolling institution.
• Patients must have esophageal, gastric or GEJ adenocarcinoma with HER2 overexpression and/oramplification as determined by immunohistochemistry (IHC 3+) or fluorescent in situ hybridization (FISH+ as defined as HER2:CEP17 ratio ≥2.0 if IHC 2+). No central testing will be required. The testing can be performed on archival tissue that is less than 6 months old. If archival tissue is more than 6 months old, a new biopsy must be obtained to confirm HER2 status prior to enrollment.
• Patients may have received no prior chemotherapy or be treatment naïve for stage IV disease. Patients may have received prior adjuvant therapy (chemotherapy and/or chemoradiation) if more than 6 months have elapsed between the end of adjuvant therapy and expected date of treatmentstart on this study. Patients who have received maintenance nivolumab after chemoradiation and surgery would be eligible as long as the last dose of nivolumab was more than 3 months from thedate of expected date of treatment start on this study.
• Patients must have measurable disease per RECIST v1.1.
• Patients must not have active decompensated cardiomyopathy and must have a normal LVEF (≥ 53%). If a patient has a borderline LVEF (40-52%), they may be considered after consultation with cardiology and study PI.
• ECOG performance status 0 or 1.
• Demonstrate adequate organ function as outlined in protocol.
• Female patients of childbearing potential should have a negative urine or serum pregnancy within 72hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required.
• Female patients of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication. Patients of childbearing potential are those who have not been surgically sterilized or have not been free from menses for > 2 years.
• Male patients should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy.
• Participants with treated brain metastases are eligible if follow-up brain imaging after central nervous system- (CNS-) directed therapy shows no evidence of progression at 4-6 weeks after treatment.
• Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

• Currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational treatment within 4 weeks of the first dose of treatment.
• Has had prior chemotherapy, targeted small molecule therapy, immunotherapy prior to study Day 1 for metastatic disease or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent with the exception of alopecia or immune mediated hypothyroidism.

Note: (a) If patient received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. (b.) If patient received radiation treatment for brain metastases, then it should have completed more than 6 weeks prior to starting Day 1 of treatment.

• Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis.
• Has active autoimmune disease that has required systemic therapy in the past 2 years (i.e. disease modifying agents, immunosuppressants or corticosteroids). Replacement therapy (i.e. thyroxine, insulin, physiologic doses of corticosteroids for adrenal or pituitary insufficiency etc.) is not considered a form of systemic therapy and is allowed.
• Has a diagnosis of immunodeficiency or receives chronic steroid therapy (in doses exceeding prednisone 10 mg/day equivalent).
• Has history of non-infectious pneumonitis that required steroids or current pneumonitis.
• Has an active infection requiring systemic therapy.
• Has baseline neuropathy > grade 1.
• Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator.
• Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.
• Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment.
• Has had COVID-19 infection within 90 days of confirming eligibility or has sequelae of COVID-19 infection such as symptoms that cannot be explained by any other medical event or comorbidity.
• Vaccination for COVID-19 is allowed on the study unless patient had a grade 3 event after either dose of the vaccine and has not resolved to grade 1 before registration.
• Is unwilling to give written informed consent, unwillingness to participate, or inability to comply with the protocol for the duration of the study.
• Has active or clinically significant cardiac disease including: (a.) Congestive heart failure - New York Heart Association (NYHA) > Class II. (b) Active coronary artery disease.(c) Cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers or digoxin.(d) Unstable angina (anginal symptoms at rest), new-onset angina within 3 months before initiation, or myocardial infarction within 6 months before initiation. (e) QTc interval >450 ms for men or >470 ms for women or known history of QTc prolongationor Torsades de Pointes.
• Patient has significant chronic gastrointestinal disorder with diarrhea as a major symptom (e.g.,Crohn's disease, malabsorption, or Grade ≥2 (NCI CTCAE v.5.0) diarrhea of any etiology at screening).