Physician/Patient Choice of Either High-Dose Recombinant Interferon Alfa-2B or Ipilimumab, Versus Pembrolizumab in Treating Patients With Stage III-IV High Risk Melanoma That Has Been Removed by Surgery

Inclusion Criteria: * STEP 1 REGISTRATION: * Patients must have completely resected melanoma of cutaneous origin or of unknown primary in order to be eligible for this study; patients must be classified as stage IIIA (N2a), IIIB, IIIC, or stage IV melanoma; patients with non-ulcerated T1b N1a disease are not eligible; patients with melanoma of mucosal or other non-cutaneous origin are eligible; patients with melanoma of ocular origin are not eligible; patients with a history of brain metastases are ineligible * Patients are eligible for this trial either at initial presentation of their melanoma or at the time of the first detected nodal, satellite/in-transit, distant metastases, or recurrent disease in prior lymphadenectomy basin or distant site; nodal, satellite/in-transit metastasis, distant metastases or disease in a prior complete lymphadenectomy basin must have been confirmed histologically by hematoxylin and eosin (H \& E) stained slides * Patients with multiple regional nodal basin involvement are eligible; gross or microscopic extracapsular nodal extension is permitted * Patients at initial presentation of melanoma must undergo an adequate wide excision of the primary lesion, if present; patients with previously diagnosed melanoma must have had all current disease resected with pathologically negative margins and must have no evidence of disease at the primary site or must undergo re-resection of the primary site; a full lymphadenectomy meeting the criteria outlined…