Trial of mFOLFOX6 + Trastuzumab + Avelumab in Gastric and Esophageal Adenocarcinomas

Inclusion Criteria: 1. Written informed consent and HIPAA authorization for release of personal health information prior to registration. 2. Age ≥ 18 years at the time of consent. 3. ECOG Performance Status of 0 or 1. 4. Histologically confirmed esophageal, gastroesophageal junction, or gastric adenocarcinoma, with unresectable or metastatic disease documented on diagnostic imaging studies. 5. HER2 amplification confirmed by standard of care testing of tumor specimen (3+ by immunohistochemistry, or 2+ on IHC with ISH with HER2/CEP17 ratio ≥2). 6. Radiographically measurable disease according to RECIST 1.1 within 28 days prior to registration. 7. Adequate organ function as defined in the table below. All screening labs to be obtained within 28 days prior to registration. * Absolute Neutrophil Count ≥ 1.5 x 10\^9/L * Hemoglobin (Hgb) ≥ 9 g/dL (may have been transfused) * Platelets ≥ 100 x 10\^9/L OR ≥ 75 x 10\^9/L for patients who received Cycle 1 of mFOLFOX6 +/- trastuzumab prior to registration * Calculated creatinine clearance1 ≥ 30 mL/min OR creatinine ≤ 1.5 × upper limit of normal (ULN) * Bilirubin ≤ 1.5 × upper limit of normal (ULN) (Subjects with Gilbert's syndrome may be enrolled despite a total bilirubin level \>1.5 mg/dL, if their conjugated bilirubin is \< 1.5× ULN) * Aspartate aminotransferase (AST) ≤ 2.5 × ULN OR ≤ 5x ULN in patients with known liver metastases * Alanine aminotransferase (ALT) ≤ 2.5 × ULN OR ≤ 5x ULN in patients with known liver metastases 8. Left ventricular ejection fraction (LVEF) ≥ 50% or above the lower limit of the institutional normal range, whichever is lower. 9. Females of childbearing potential must have a negative serum pregnancy test at screening. NOTE: Females are considered of child bearing potential unless they are surgically sterile (have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or they are naturally postmenopausal for at least 12 consecutive months. 10. Females of childbearing potential and males must be willing to abstain from heterosexual activity or to use 2 forms of effective methods of contraception from the time of informed consent until 210 days after treatment discontinuation. The two contraception methods can be comprised of two barrier methods, or a barrier method plus a hormonal method. 11. As determined by the enrolling physician or protocol designee, ability of the subject to understand and comply with study procedures for the entire length of the study. Exclusion Criteria: 1. Previous systemic therapy for stage IV disease - EXCEPT that patient may have received one cycle of mFOLFOX6 +/- trastuzumab within the 4 weeks prior to registration. 2. Active infection requiring intravenous systemic therapy. 3. Pregnant or breastfeeding (NOTE: breast milk cannot be stored for future use while the mother is being treated on study). 4. Treatment with any investigational drug within 28 days prior to registration. 5. Prior immune checkpoint inhibitor therapy (i.e. anti-CTLA-4, anti-PD-L1, anti-PD-1), or HER2-directed therapy (including trastuzumab) 6. Evidence of interstitial lung disease or active, non-infectious pneumonitis 7. Untreated brain metastasis or brain metastasis treated within 4 weeks prior to enrollment. 8. Known additional malignancy that is active and/or progressive requiring treatment; exceptions include basal cell or squamous cell skin cancer, in situ cervical or bladder cancer, or other cancer for which the subject has been disease-free for at least five years. 9. Serious cardiovascular event within 6 months prior to study entry, including myocardial infarction, malignant hypertension, severe/unstable angina, symptomatic congestive heart failure (≥ New York Heart Association Classification Class II), cerebral vascular accident, transient ischemic attack, or serious cardiac arrhythmia requiring medication. 10. History of organ allograft or allogeneic stem cell transplantation 11. Active autoimmune disease requiring systemic treatment in the past 3 months (for example with disease modifying agents, corticosteroids, or immunosuppressive drugs). Exceptions Include: * Subjects with endocrine diseases stable on replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) or hormone suppression. * Subjects that require intermittent use of bronchodilators, local steroid injections, or inhaled or topical steroids * Subjects with vitiligo, psoriasis, Sjogren's syndrome, or resolved childhood asthma/atopy 12. Current use of immunosuppressive medication, EXCEPT for the following: a. intranasal, inhaled, topical steroids, or local steroid injection (e.g., intra-articular injection); b. Systemic corticosteroids at physiologic doses ≤ 10 mg/day of prednisone or equivalent; c. Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication). 13. Known history of testing positive for HIV or known acquired immunodeficiency syndrome. 14. Known history of Hepatitis B virus (HBV) or hepatitis C virus (HCV) infection. Subjects with laboratory evidence of cleared HBV and HCV infection will be permitted. 15. Vaccination within 4 weeks of the first dose of avelumab and while on trials is prohibited except for administration of inactivated vaccines. 16. Known prior severe hypersensitivity to investigational product or any component in its formulations, including known severe hypersensitivity reactions to monoclonal antibodies (NCI CTCAE v5 Grade ≥ 3). 17. Persisting toxicity related to prior therapy (NCI CTCAE v5 Grade \> 1); however, alopecia, sensory neuropathy Grade ≤ 2, or other Grade ≤ 2 not constituting a safety risk based on investigator's judgment are acceptable. 18. Other severe acute or chronic medical conditions including immune colitis, inflammatory bowel disease, immune pneumonitis, pulmonary fibrosis or psychiatric conditions including recent (within the past year) or active suicidal ideation or behavior; or laboratory abnormalities that may increase the risk associated with study participation or study treatment administration or may interfere with informed consent, the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for entry into this study.