Nivolumab or Expectant Observation Following Ipilimumab, Nivolumab, and Surgery in Treating Patients With High Risk Localized, Locoregionally Advanced, or Recurrent Mucosal Melanoma

You may be eligible if

• STEP 1 ELIGIBILITY CRITERIA
• Documentation of disease:
• * Histologic documentation: histologically proven mucosal melanoma by local pathology
• * Tumor tissue: tumor tissue from the primary site of disease must be available for PD-L1 testing (stratification factor)
• Disease status
• * Tumors must have NOT been completely resected, or must be locoregionally recurrent if previously resected; tumor must be deemed potentially resectable by local surgeon
• * MM arising from the head/neck, genitourinary, or gastrointestinal tract
• * Disease meets any 1 of 4 characteristics:
• * Regional lymph node (LN) involvement; OR
• * Multifocal/satellite primary disease; OR
• * Single localized, primary disease meeting one of the following site-specific requirements:
• * Head/neck - any primary lesion if sinonasal; pT4a or above for nasal or oral cavity
• * Anorectal - any primary lesion
• * Conjunctiva - any primary lesion T2 or T3 stage by American Joint Committee on Cancer (AJCC)
• * Vaginal/cervical - any primary
• * Vulvar (hair bearing surface, labia majora) - AJCC cutaneous stage IIB or higher
• * Esophageal - any primary
• * Locoregionally recurrent following prior resection
• * No evidence of metastatic disease at the time of registration
• No prior medical therapy (chemotherapy, immunotherapy, biologic or targeted therapy) or radiation therapy for MM, unless locoregionally recurrent; if recurrent, no prior medical or radiation therapy is allowed for the latest recurrence
• No history of the following:
• * Active known or suspected autoimmune disease
• * Human immunodeficiency virus (HIV) with CD4+ count \< 300 or detectable viral load; patients with HIV, undetectable viral load, and CD4+ count \>= 300 are eligible
• * Known active hepatitis B or C
• * Hepatitis B can be defined as:
• * Hepatitis B virus surface antigen (HBsAg) \> 6 months
• * Serum hepatitis B virus (HBV) deoxyribonucleic acid (DNA) 20,000 IU/ml (105 copies/ml), lower values 2,000-20,000 IU/ml (104-105 copies/ml) are often seen in hepatitis B virus e antigen (HBeAg)-negative chronic hepatitis B
• * Persistent or intermittent elevation in alanine aminotransferase (ALT)/aspartate aminotransferase (AST) levels
• * Liver biopsy showing chronic hepatitis with moderate or severe necroinflammation
• * Hepatitis C can be defined as:
• * Hepatitis C antibody (AB) positive
• * Presence of hepatitis C virus (HCV) RNA
• * Known active pulmonary disease with hypoxia defined as oxygen saturation \< 85% on room air
• Not pregnant and not nursing
• * For women of childbearing potential only, a negative pregnancy test done =\< 14 days prior to registration is required
• Eastern Cooperative Oncology Group (ECOG) performance status =\< 2
• Absolute neutrophil count (ANC) \>= 1,500/mm\^3
• Platelet count \>= 100,000/mm\^3
• Creatinine clearance \>= 30 mL/min by Modified Diet in Renal Disease (MDRD) equation or Cockcroft-Gault
• Total bilirubin =\< 1.5 x upper limit of normal (ULN)
• * Except in case of Gilbert disease
• AST/ALT =\< 2.5 x upper limit of normal (ULN)
• Thyroid-stimulating hormone (TSH) within normal limits (WNL)
• * Supplementation is acceptable to achieve a TSH WNL; in patients with abnormal TSH if free T4 is normal and patient is clinically euthyroid, patient is eligible
• Concomitant medications
• * No systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 7 days of registration (inhaled steroids for patients with underlying chronic pulmonary disease is acceptable as long as they meet other eligibility as listed above)
• * No other planned concurrent investigational agents or other tumor directed therapy (chemotherapy, radiation) while on study
• STEP 2 ELIGIBILITY CRITERIA
• Surgical resection of all gross disease
• * This assessment will be made by the local investigator based on review of the operative report, pathology results, and/or radiology reports; microscopically positive margins (e.g. R1 resection) are permitted
• Completion of PD-L1 testing
• * Patients will be stratified as PD-L1 \>= 5% versus (vs) \< 5% OR inevaluable; baseline tumor will be utilized; if this returns inevaluable, efforts should be made to utilize the resected specimen
• Randomization within 112 days of completion of surgical
• * The primary region must be included on cross-sectional imaging (e.g. sinus/neck if arising from sinonasal primary; pelvis if genitourinary); radiographic changes considered nonspecific or possibly due to surgery or radiation are not considered evidence of disease
• No significant immune-related adverse event due to the nivolumab plus ipilimumab dose received in the neoadjuvant setting, as follows:
• * Any grade myocarditis, including an asymptomatic troponin elevation felt to be related to nivolumab plus ipilimumab
• * Any grade neurologic complication (e.g. meningitis, encephalitis, neuropathy); study chair should be contacted if there is any question whether an adverse event (AE) was neurologic in nature
• * Grade 2 or higher pneumonitis
• * Grade 2 colitis
• * Grade 2 or higher anemia (due to drug; unrelated anemia is not exclusionary)
• * Thyroid/adrenal AEs regardless of grade that have stabilized or are clinically asymptomatic are eligible
• * Fatigue, regardless of grade, is not a contraindication to randomization
• * Grade 4 AST or ALT elevation
• * Asymptomatic elevated amylase and lipase, regardless of grade, are not contraindications to randomization
• * Grade 4 rash; grade 3 rash is not a contraindication to randomization; any oropharyngeal lesions or bullous skin lesions that are suggestive of toxic epidermal necrolysis or Stevens-Johnson syndrome are contraindications to randomization regardless of the grade of rash
• * If not specified above, other Common Terminology Criteria for Adverse Events (CTCAE) grade 3 or higher AEs deemed possibly related to the nivolumab plus ipilimumab are exclusions to randomization; AEs that were attributable to surgery or adjuvant RT would not be contraindications to randomization