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 bilirubin =\< 1.5 x upper limit of normal (ULN) (obtained =\< 30 days prior to registration) * REGISTRATION: Alanine aminotransferase (ALT) AND aspartate transaminase (AST) =\< 1.5 x ULN (obtained =\< 30 days prior to registration) * REGISTRATION: Prothrombin time (PT)/international normalized ratio (INR)/activated partial thromboplastin time (aPTT) =\< 1.5 x ULN OR if patient is receiving anticoagulant therapy, then INR or aPTT is within target range of therapy (obtained =\< 30 days prior to registration) * REGISTRATION: Calculated creatinine clearance \>= 40 ml/min using the Cockcroft-Gault formula (obtained =\< 30 days prior to registration) * REGISTRATION: Negative pregnancy test done =\< 8 days prior to registration, for persons of childbearing potential only * REGISTRATION: Provide written informed consent * REGISTRATION: Willingness to provide mandatory blood specimens for correlative research * REGISTRATION: Willingness to provide mandatory tissue specimens for correlative research * REGISTRATION: Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study) Exclusion Criteria: * PRE-REGISTRATION: 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 * PRE-REGISTRATION: Any of the following prior therapies: IL-2 or chronic corticosteroids, or immunosuppressive agents * NOTE: Inhaled corticosteroids are allowed * PRE-REGISTRATION: 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 * PRE-REGISTRATION: Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy * PRE-REGISTRATION: Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Or psychiatric illness/social situations that would limit compliance with study requirements * Autoimmune disease * PRE-REGISTRATION: Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * PRE-REGISTRATION: Active second malignancy currently receiving systemic treatment =\< 6 months prior to pre-registration * 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 * REGISTRATION: Identification of non-peritoneal metastasis during laparoscopy * REGISTRATION: 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 * REGISTRATION: Any of the following therapies: prior immune checkpoint inhibitors, prior IL-2, or chronic corticosteroids or immunosuppressive agents * NOTE: Inhaled corticosteroids are allowed. One-time antiemetic dose is allowed * REGISTRATION: 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 * REGISTRATION: Immunocompromised patients and patients known to be HIV positive and currently receiving antiretroviral therapy * REGISTRATION: Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Or psychiatric illness/social situations (e.g., substance abuse) that would limit compliance with study requirements * Autoimmune disease requiring systemic treatment * Small bowel obstruction * REGISTRATION: Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * REGISTRATION: History of myocardial infarction =\< 6 months prior to registration, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias * REGISTRATION: Small bowel obstruction \< 15 days prior to registration