This randomized phase III trial studies ipilimumab to see how well it works compared to high-dose interferon alfa-2b in treating patients with high-risk stage III-IV melanoma that has been removed by surgery. Immunotherapy with monoclonal antibodies, such as ipilimumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Interferon alfa-2b may interfere with the growth of tumor cells and slow the growth of melanoma and other cancers. It is not yet known whether ipilimumab is more effective than interferon alfa-2b in treating patients with melanoma.

PRIMARY OBJECTIVES: I. To evaluate recurrence-free survival (RFS) between patients randomized to receive post-operative adjuvant ipilimumab given at either 10 mg/kg (high dose ipilimumab; HIP) or 3 mg/kg (low dose ipilimumab: LIP) versus those randomized to receive high-dose interferon alfa-2b (HDI) utilizing a hierarchical design assessing HIP versus HDI first and LIP versus HDI second (if the first comparison is significant). II. To evaluate overall survival (OS) between patients randomized to receive post-operative adjuvant ipilimumab given at either 10 mg/kg (HIP) or 3 mg/kg (LIP) versus those randomized to receive HDI utilizing a hierarchical design assessing HIP versus HDI first and LIP versus HDI second (if the first comparison is significant). SECONDARY OBJECTIVES: I. To evaluate safety and tolerability of post-operative adjuvant ipilimumab therapy given at either 10 mg/kg (HIP) or 3 mg/kg (LIP). II. Among patients enrolled by Clinical Community Oncology programs (CCOPs), to compare the global quality of life (QOL) between the ipilimumab arms versus HDI using Functional Assessment of Cancer Therapy (FACT)-General (G) form and to evaluate the effect of treatment-related side effects that may have an impact on the health-related domains of QOL using Functional Assessment of Chronic Illness Therapy (FACIT)-diarrhea (D) and FACT-biological response modifiers (BRM). OUTLINE: Patients age \>= 18 are randomized to Arms A, B, or C and patients ages 12-17 are randomized to Arms D, E, or F. ARM A: Patients receive induction high-dose ipilimumab intravenously (IV) over 90 minutes on day 1. Treatment repeats every 21 days for a total of 4 cycles in the absence of disease progression or unacceptable toxicity. Beginning on week 24, patients receive maintenance high-dose ipilimumab IV over 90 minutes on day 1. Treatment repeats every 90 days for a maximum of 4 cycles in the absence of disease progression or unacceptable toxicity. (closed accrual as of 4/4/14) (adult accrual has completed to Arms A, B, and C as of 8/15/2014) ARM B: Patients receive induction high-dose recombinant interferon alfa-2b IV over 20 minutes on days 1-5, 8-12, 15-19, and 22-26 in the absence of disease progression or unacceptable toxicity. Patients then receive maintenance high-dose recombinant interferon alfa-2b subcutaneously (SC) on days 1, 3, and 5. Treatment repeats every week for 48 weeks in the absence of disease progression or unacceptable toxicity. (adult accrual has completed to Arms A, B, and C as of 8/15/2014) ARM C: Patients receive induction low-dose ipilimumab IV over 90 minutes on day 1. Treatment repeats every 21 days for a total of 4 cycles in the absence of disease progression or unacceptable toxicity. Beginning on week 24, patients receive maintenance low-dose ipilimumab IV over 90 minutes on day 1. Treatment repeats every 90 days for a maximum of 4 cycles in the absence of disease progression or unacceptable toxicity. (adult accrual has completed to Arms A, B, and C as of 8/15/2014) ARM D: Patients receive induction high-dose ipilimumab IV over 90 minutes on day 1. Treatment repeats every 21 days for a total of 4 cycles in the absence of disease progression or unacceptable toxicity. Beginning on week 24, patients receive maintenance high-dose ipilimumab IV over 90 minutes on day 1. Treatment repeats every 90 days for a maximum of 4 cycles in the absence of disease progression or unacceptable toxicity. ARM E: Patients receive induction high-dose recombinant interferon alfa-2b IV over 20 minutes on days 1-5, 8-12, 15-19, and 22-26 in the absence of disease progression or unacceptable toxicity. Patients then receive maintenance high-dose recombinant interferon alfa-2b SC on days 1, 3, and 5. Treatment repeats every week for 48 weeks in the absence of disease progression or unacceptable toxicity ARM F: Patients receive induction low-dose ipilimumab IV over 90 minutes on day 1. Treatment repeats every 21 days for a total of 4 cycles in the absence of disease progression or unacceptable toxicity. Beginning on week 24, patients receive maintenance low-dose ipilimumab IV over 90 minutes on day 1. Treatment repeats every 90 days for a maximum of 4 cycles in the absence of disease progression or unacceptable toxicity. After completion of study therapy, patients are followed up every 3 months for 2 years, every 6 months for 3 years, and then yearly for up to 15 years.