Phase II Trial of Pembrolizumab With Trastuzumab and Chemotherapy in Advanced HER2 Positive Esophagogastric (EG) Cancer

Inclusion Criteria: * Patient must have pathologically or cytologically MSKCC confirmed esophageal, gastric or gastroesophageal junction (GEJ) adenocarcinoma by the enrolling institution. * Patients must have esophageal, gastric or gastroesophageal adenocarcinoma with HER2 overexpression and/or amplification as determined by next generation sequencing assay, immunohistochemistry (IHC 3+) or fluorescent in situ hybridization (FISH+ is defined as HER2:CEP17 ratio ≥ 2.0). MSKCC or enrolling institution confirmation of HER2 status is not mandatory prior to enrollment and treatment on study. For patients with outside HER2 testing, if sufficient tissue is available HER2 testing will be repeated at MSKCC or enrolling institution for purpose of analysis and will not impact the patient's eligibility. * Additional available archival tumor tissue in the form of 15-20 unstained slides should be submitted to MSKCC for future correlative analysis, but will not be required prior registration. Note: if tissue is depleted, patient will still be eligible after discussion with the MSK PI. * Patients may have received no prior chemotherapy 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 registration * Patients must have disease that can be evaluated radiographically. This may be measurable disease or non-measurable disease per RECIST 1.1. * Patient 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 and treated per the guidelines in section 11.2.2. * Age 18 years or older. * ECOG performance status 0-2. * Demonstrate adequate organ function as defined below. All screening labs should be performed within 10 days of treatment initiation. Hematological Absolute neutrophil count (ANC) ≥1,500 /mcL Platelets ≥100,000 / mcL Hemoglobin ≥9 g/dL or ≥5.6 mmol/L Renal Serum creatinine ≤1.5 X upper limit of normal (ULN) OR Measured or calculated creatinine clearance (measured via 24-hour urine collection) ≥60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN (GFR can also be used in place of creatinine or CrCl) Hepatic Serum total bilirubin ≤ 1.5 X ULN (1.5 mg/dL or 25.65 μmol/L) OR Direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 ULN. Except patients with Gilbert's disease (≤3x ULN) AST (SGOT) and ALT (SGPT) ≤ 2.5 X ULN OR AST (SGOT) and ALT (SGPT) ≤ 5 X ULN for subjects with liver metastases Albumin \>2.5 mg/dL Coagulation Prothrombin Time (PT) ≤1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants Activated Partial Thromboplastin Time (aPTT) ≤1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours 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 subjects 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. Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year. * Male subjects 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. * Peripheral neuropathy ≤grade 1 Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment. * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. * Has a known history of active TB (Bacillus tuberculosis) * Hypersensitivity to pembrolizumab or any of its excipients. * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent. (Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy.) * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. * Has known history of, or any evidence of active, non-infectious pneumonitis. * Has an active infection requiring systemic therapy. * 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 received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. * Active or prior documented autoimmune or inflammatory disorder (including inflammatory bowel disease; systemic lupus erythematosus; Wegener syndrome \[granulomatosis with polyangiitis\]; myasthenia gravis; Graves' disease; rheumatoid arthritis, hypophysitis, uveitis) within the past 3 years prior to the start of treatment. The following are exceptions to this criterin: * Subjects with vitiligo or alopecia * Subjects with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement or psoriasis not requiring systemic treatment. * Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). * Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Has received a live vaccine within 30 days of planned start of study therapy. (Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed.) * 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: Congestive heart failure - New York Heart Association (NYHA) \> Class II. Active coronary artery disease. Cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers or digoxin. Unstable angina (anginal symptoms at rest), new-onset angina within 3 months before initiation, or myocardial infarction within 6 months before initiation.