Phase II Study of Ramucirumab With Chemotherapy in Patients With Metastatic Gastroesophageal Junction and Gastric Cancer

Inclusion Criteria: * Patients must have pathologically or cytologically MSKCC confirmed diagnosis of gastric or GEJ adenocarcinoma. * Patients must have Stage IV gastric or GEJ 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 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 for purpose of analysis and will not impact the patient's eligibility. * Available archival tumor tissue should be submitted to MSKCC for IMPACT analysis, but will not be required prior to registration. Note: if tissue is depleted, patient will still be eligible after discussion with the PI. * Patients must have disease that can be evaluated radiographically. This may be measurable disease or non-measurable disease per RECIST 1.1. * 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. * Age of 18 years or older. * ECOG performance status 0-1. * Peripheral neuropathy ≤ grade 1 * Patients who have adequate hepatic function as defined by a total bilirubin ≤1.5 times upper limit of institutional normal value (ULN) mg/dL (except patients with Gilbert's disease), and aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 3.0 times ULN or ≤ 5.0 times the ULN in the setting of liver metastases. * Patients who have adequate hematologic function, as evidenced by absolute neutrophil count (ANC) ≥1500/μL, hemoglobin ≥9 g/dL (5.58 mmol/L), and platelets ≥100,000/μL. * Patients who have adequate renal function as defined by calculated creatinine clearance ≥60 mL/minute using the Cockcroft-Gaul formula or equivalent method. * Patients whose urinary protein is ≤2+ on routine urinalysis (UA; if routine analysis is \>2+, a 24-hour urine collection for protein must demonstrate \<2g of protein in 24 hours to allow participation in this protocol). * The patient must have adequate coagulation function as defined by International Normalized Ratio (INR) ≤ 1.5, and a partial thromboplastin time (PTT) ≤ 5 seconds above the ULN (unless receiving anticoagulation therapy). Patients receiving warfarin must be switched to low molecular weight heparin and have achieved stable coagulation profile prior to first dose of protocol therapy. * Patients, must be postmenopausal, surgically sterile, or using effective contraception (hormonal or barrier methods). * Female patients of childbearing potential must have a negative serum pregnancy test within 7 days of study entry. Exclusion Criteria: * Patients who have uncontrolled or poorly-controlled hypertension (\>160 mmHg systolic or \>100 mmHg diastolic for \>4 weeks) despite standard medical management. * Patients receiving any concurrent anticancer therapy or investigational agents with the intention of treating gastric/GEJ cancer. Previously received trastuzumab as part of a regimen in the metastatic setting with evidence of progression. 89Zr-trastuzumab use as imaging agent for 89Zr-trastuzumab PET permitted. * Patients having: * Cirrhosis at a level of Child-Pugh B (or worse) or * Cirrhosis (any degree) and a history of hepatic encephalopathy or clinically meaningful ascites resulting from cirrhosis. Clinically meaningful ascites is defined as ascites from cirrhosis requiring diuretics or paracentesis. * Active or clinically significant cardiac disease including: * Congestive heart failure - New York Heart Association (NYHA) \> Class II. * Active coronary artery disease. * Left ventricular function \<50%. * 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 randomization, or myocardial infarction within 6 months before randomization. * Patients who have experienced any arterial thromboembolic events, including but not limited to myocardial infarction, transient ischemic attack, cerebrovascular accident, or unstable angina, within 6 months prior to enrollment. * Patients who are receiving chronic antiplatelet therapy, including aspirin, nonsteroidal anti-infalmmatory drugs (NSAIDs, inluding ibuprofen, naproxen, and others), dipyridamole or clopidogrel, or similar agents. Once-daily aspirin (maximum dose 325 mg/day is permitted. * Evidence or history of bleeding diathesis or coagulopathy. * Patients who have experienced any Grade 3-4 GI bleeding within 3 months prior to enrolment. * Unwillingness to give written informed consent, unwillingness to participate, or inability to comply with the protocol for the duration of the study. * Patients with prior trastuzumab treatment. * Patients with known active brain or central nervous system metastases, including leptomeningeal disease. Patients with treated and asymptomatic brain metastases may be eligible after discussion with PI. * Patients who are pregnant or breast-feeding. * Patients with a serious or nonhealing wound, ulcer, or bone fracture within 28 days prior to enrollment. * The patient has undergone major surgery within 28 days prior to first dose of protocol therapy * Patients may not have had major surgical procedure within 2 weeks of registration. * Patients who have elective or planned major surgery to be performed during the course of the clinical trial.Minor surgery/subcutaneous venous access device placement within 7 days prior to first dose of protocol therapy is permitted. * Patients may not have had radiation within 28 days prior to first dose weeks of registration. * Patients may not have any other medical condition or reason, in that investigator's opinion, makes the patient unstable to participate in a clinical trial.