Hyperthermic Intraperitoneal Chemotherapy With Cisplatin and Paclitaxel for the Treatment of Patients With Gastric and Gastroesophageal Junction Adenocarcinoma at High Risk of Peritoneal Recurrence

Inclusion Criteria: * Age ≥ 18 and ≤ 80 years * Histological confirmation of adenocarcinoma of the stomach or gastroesophageal junction (GEJ) (Siewert type II or III) * Tumor index (TI) ≥ 90 (T stage multiplied by the largest tumor diameter in mm on endoscopic ultrasound \[EUS\]). Patients with linitus plastica automatically have TI ≥ 90 * Hemoglobin ≥ 8.0 g/dL * Absolute neutrophil count (ANC) ≥ 1000/mm\^3 * Platelet count ≥ 75,000/mm\^3 * Calculated creatinine clearance ≥ 60 ml/min using the Cockcroft-Gault formula * No radiographic or histological evidence of distant metastasis * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * Willingness to provide mandatory blood specimens for correlative research * Willingness to provide mandatory tissue specimens for correlative research * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) Exclusion Criteria: * Any of the following because this study involves an agent that has known genotoxic, mutagenic, and teratogenic effects: * Pregnant persons * Nursing persons * Persons of childbearing potential and persons able to father a child who are unwilling to employ adequate contraception * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Renal insufficiency (estimated glomerular filtration rate \[eGFR\] \< 60) * Or psychiatric illness/social situations that would limit compliance with study requirements * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Active second malignancy currently receiving systemic treatment ≤ 6 months prior to pre-registration * History of myocardial infarction ≤ 6 months prior to pre-registration, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias