Futibatinib With Paclitaxel and Ramucirumab for the Treatment of Locally Advanced or Unresectable Gastric, Gastroesophageal Junction, or Esophageal Adenocarcinoma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed locally advanced/unresectable gastric, gastroesophageal junction, or esophageal adenocarcinoma that is microsatellite stable and HER2 negative. (American Joint Committee on Cancer \[AJCC\] staging criteria; https://pmc.ncbi.nlm.nih.gov/articles/PMC5387145/) * Note: Histological or cytological test reports from external laboratories outside of Northwestern University (NU) will also be accepted * Patients must have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Note: Patients must have documented unresectable and/or metastatic disease on CT or MRI imaging completed prior to registration. Imaging must have been completed within 90 days prior to registration for participants with measurable disease * Patients must not have received more than 1 prior line of therapy in the metastatic setting. * Note: Patients who have received neoadjuvant or adjuvant therapy must have completed therapy a year prior to registration in this study. Exception: patients with neoadjuvant or adjuvant therapy who have progressed within 6 months * Patients must be age ≥ 18 years * Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Leukocytes (white blood cells \[WBC\]) ≥ 2,000/mcL * Absolute neutrophil count (ANC) ≥ 1500/mcL * Hemoglobin (Hgb) ≥ 9 g/dL (transfusions within 1 week of registration are not allowed to meet cutoff) * Platelets (PLT) ≥ 100,000/mcL (transfusions within 1 week of registration are not allowed to meet cutoff) * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) ≤ 3 x institutional ULN (unless liver metastases are present, in which case they must be ≤ 5 x ULN) * Alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 x institutional ULN (unless liver metastases are present, in which case they must be ≤ 5 x ULN) * Creatinine ≤ 1.5 x Institutional ULN or meeting creatinine clearance (CrCl) criteria below * Creatinine clearance per the Cockcroft-Gault formula or 24-hour urine collection) ≥ 45 mL/min * Phosphate \< ULN * International normalized ratio (INR) \< 1.5 * Patient's urinary protein is ≤ 1+ on dipstick or routine urinalysis (UA) within 28 days of registration. * Note: Random analysis of urine protein with a normal value is sufficient. If urine dipstick or routine analysis indicated proteinuria ≥ 2+, then a 24-hour urine is to be collected and demonstrate \< 1000 mg of protein in 24 hours to allow participation in the study * For patients with a known history of human immunodeficiency virus (HIV), infected patients on effective anti-retroviral therapy must have a viral load undetectable for 6 months prior to registration. * Please note: this lab is not a requirement for eligibility, however, if it has been completed previously as part of the patient's health care, it should be documented for eligibility * Patients with known history of chronic hepatitis B virus (HBV) infection must be on suppressive therapy with an undetectable viral load. * Please note: this lab is not a requirement for eligibility, however if it has been completed previously as part of the patient's health care, it should be documented for eligibility * Patients with a known history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with a known HCV infection who are currently on treatment are eligible if they have an undetectable HCV viral load. * Please note: this lab is not a requirement for eligibility, however if it has been completed previously as part of the patient's health care, it should be documented for eligibility * Patients with treated brain metastases must not have any evidence of progression on the follow-up brain imaging after central nervous system (CNS)-directed therapy. * Note: All treatment for brain metastases must have been completed at least 28 days prior to registration * Futibatinib and other therapeutic agents used in this trial are known to be teratogenic. For this reason, patients of child-bearing potential (POCBP) and their partners with sperm-producing reproductive capacity must agree to use adequate contraception from time of informed consent, for the duration of study participation, and for 3 months following completion of study drug therapy. Should a POCBP become pregnant or suspect they are pregnant while they or their partner are participating in this study, they should inform their treating physician immediately. Patients with sperm-producing reproductive capacity (PWSPRC) treated or enrolled on this protocol must also agree to use adequate contraception with partners of childbearing potential from time of informed consent, for the duration of study participation, and 3 months after completion of study drug administration * Note: A POCBP is any patient (regardless of gender, sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) with an egg-producing reproductive tract who meets the following criteria: * Has not undergone a hysterectomy or bilateral oophorectomy * Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for \> 12 months) * POCBP must have a negative pregnancy test prior to registration on study * Patients must have the ability to understand and the willingness to sign a written informed consent document and comply with the study requirements * Patients must have the ability to swallow, retain and absorb oral medications Exclusion Criteria: * Patients with adenosquamous or mixed histology disease * Patients who have received/are receiving other investigational agents, or anticancer/antineoplastic therapy including chemotherapy, immunotherapy, biological response modifiers, anti-neoplastic endocrine therapy or devices concurrently or within 21 days or 5 times the half-life, whichever is shorter, prior to first dose of cycle 1 * Patients who have previously received a FGFR inhibitor. * Note: Agents that are multi-kinase inhibitors are allowed * Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) with the exception of alopecia, neuropathy and other non-significant adverse events per NCI CTCAE v 6.0 * Patients who have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to paclitaxel, ramucirumab, or futibatinib * Patients who have major surgical procedure planned during the study or any surgery within 28 days of registration or any subcutaneous venous access device placement within 7 days prior registration * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, or who have experienced arterial thromboembolic events, including but not limited to myocardial infarction, transient ischemic attack, cerebrovascular accident, or unstable angina, within 6 months prior to registration ,should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. * Note: To be eligible for this trial, patients should be class 2B or better * History of gastrointestinal perforation and/or fistulae within 6 months prior to registration * History of active bleeding or significant gastrointestinal (GI) bleeding requiring intervention within 60 days prior to registration * History and/or current evidence of endocrine alteration of calcium-phosphorus homeostasis. History and/or current evidence of ectopic mineralization/calcification including but not limited to soft tissue, kidneys, intestine, or myocardia and lung with the exception of calcified lymph nodes and asymptomatic arterial calcification * Current evidence of retinal disorder/keratopathy including but not limited to bullous/band keratopathy, corneal abrasion, inflammation/ulceration, keratoconjunctivitis, etc., confirmed by ophthalmologic examination * Patients who have an uncontrolled intercurrent illness including, but not limited to any of the following: * Hypertension that is not controlled on medication(per treating physician's discretion) * Ongoing or active infection requiring systemic treatment * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Psychiatric illness/social situations that would limit compliance with study requirements * Any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints * Patients with a prior or concurrent malignancy whose natural history or treatment has the potential to interfere with the safety or activity assessment of the investigational regimen (per treating physician's discretion) * Patients who are pregnant or nursing