Nivolumab and Ipilimumab in Treating Patients With Esophageal and Gastroesophageal Junction Adenocarcinoma Undergoing Surgery

Inclusion Criteria: * STEP 1 RANDOMIZATION: Patients must be age \>= 18 years * STEP 1 RANDOMIZATION: Patients must have histologically confirmed T1N1-3M0 or T2-3N0-2M0 esophageal or gastroesophageal junctional adenocarcinoma (Siewert I and II) * STEP 1 RANDOMIZATION: Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * STEP 1 RANDOMIZATION: Patents must be deemed a surgical candidate by a thoracic surgeon, surgical oncologist, or surgeon who is qualified to perform an esophagectomy * STEP 1 RANDOMIZATION: Absolute neutrophil count \>= 1,500/mcL (within less than or equal to 14 days prior to randomization) * STEP 1 RANDOMIZATION: Platelets \>= 100,000/mcL (within less than or equal to 14 days prior to randomization) * STEP 1 RANDOMIZATION: Total bilirubin =\< institutional upper limit of normal (ULN) (within less than or equal to 14 days prior to randomization) * STEP 1 RANDOMIZATION: Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN (within less than or equal to 14 days prior to randomization) * STEP 1 RANDOMIZATION: Serum creatinine =\< 1.5 x institutional ULN (within less than or equal to 14 days prior to randomization) * STEP 1 RANDOMIZATION: Hemoglobin (Hgb) \>= 9 g/dL (within less than or equal to 14 days prior to randomization) * STEP 1 RANDOMIZATION: Leukocytes \>= 3,000/mm\^3 (within less th…