Aldesleukin With Nivolumab and Standard Chemotherapy for Treatment of Gastric Cancer With Peritoneal Metastasis

Inclusion Criteria: * PRE-REGISTRATION: Age \>= 18 years * PRE-REGISTRATION: Disease characteristics * Histological confirmation of adenocarcinoma of the stomach or gastroesophageal junction (GEJ) * Currently receiving first-line therapy with leucovorin calcium, fluorouracil, and oxaliplatin (FOLFOX) and nivolumab without evidence of disease progression OR planning to start first-line therapy with FOLFOX and nivolumab * PRE-REGISTRATION: No radiographic or histological evidence of non-peritoneal metastasis * PRE-REGISTRATION: Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * PRE-REGISTRATION: Willingness to provide mandatory blood specimens for correlative research * PRE-REGISTRATION: Willingness to provide mandatory tissue specimens for correlative research * PRE-REGISTRATION: Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study) * REGISTRATION: Peritoneal Carcinomatosis Index (PCI) \>= 1 and =\< 24 obtained =\< 30 days prior to registration * REGISTRATION: Clinical, pathological, or radiographic evidence of peritoneal metastasis per PCI and Peritoneal Regression Grading Score (PRGS) * REGISTRATION: Hemoglobin \>= 8.0 g/dL (obtained =\< 30 days prior to registration) * REGISTRATION: Absolute neutrophil count (ANC) \>= 1000/mm\^3 (obtained =\< 30 days prior to registration) * REGISTRATION: Platelet count \>= 75,000/mm\^3 (obtained =\< 30 days prior to registration) * REGISTRATION: Total bil…