A Phase II Study of High Dose Bolus IL2 in Combination With Low Dose Ipilimumab Followed Sequentially by Nivolumab in Patients With Inoperable Stage III or Stage IV Melanoma Who Have Failed Prior Anti-PD1 Immunotherapy

Inclusion Criteria: * Histologically or cytologically confirmed metastatic melanoma. This includes American Joint Committee on Cancer (AJCC) stage IV or advanced/inoperable stage III. This also includes patients with a history of lower stage melanoma and subsequent recurrent metastatic disease that is either locally/regionally advanced/inoperable disease or distant metastases * Measurable disease, according to RECIST version 1.1 * Must be free of active brain metastasis by contrast-enhanced CT/MRI scans within 4 weeks prior to enrollment. If known to have prior brain metastases, these must have been adequately managed with standard of care radiation therapy, stereotactic radiosurgery or surgery prior to registration on the study. * Must have previously received anti-PD1 immunotherapy (nivolumab or pembrolizumab) and later experienced disease progression. * Must not have received systemic therapy or radiotherapy (including SRS) within the preceding 3 weeks. Patients must have recovered from adverse events from previous therapy by the time registration. * Must be at least 4 weeks from major surgery and have fully recovered from any effects of surgery, and must be free of significant detectable infection prior to registration. * Patients who have received prior anti-CTLA4 monoclonal antibody therapy (ipilimumab or tremelimumab) are eligible. * Patients who have previously experienced prior high-grade (grade 3 or 4 by CTCAE criteria) immune related adverse events with immune checkpoint inhibitors must be discussed with the study PI and cleared prior to enrollment on this study in order to ensure patient safety. * Patients with BRAF V600 mutant melanoma must have previously received BRAF targeted therapy for metastatic melanoma and later experienced disease progression. Patients who refuse or decline to receive BRAF targeted therapy or were intolerant of BRAF targeted therapy are eligible. * Life expectancy of greater than 3 months in the opinion of the investigator * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Must have normal organ and marrow function as specified per protocol. * Patients on full-dose anticoagulants with Prothrombin Time Test International Normalized Ratio (PT INR) \>1.5 are eligible provided that both of the following criteria are met: (a) The patient has an in-range INR (usually between 2 and 3) on a stable dose of oral anticoagulant or on a stable dose of low molecular weight heparin. (b) The patient has no active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices). * Pulmonary: Forced Expiratory Volume at 1 second (FEV1) \> 2.0 liters or \> 75% of predicted for height and age. Pulmonary function tests (PFTs) are required for patients over 50 years old or with significant pulmonary or smoking history * No evidence of congestive heart failure, symptoms of coronary artery disease, myocardial infarction less than 6 months prior to entry, serious cardiac arrhythmias, or unstable angina. * Patients who are over 40 years old or have had previous myocardial infarction greater than 6 months prior to study entry or have significant cardiac family history (CAD or serious arrhythmias) will be required to have a negative or low probability cardiac stress test (for example, thallium stress test, stress multigated acquisition scan (MUGA), stress echo or exercise stress test) for cardiac ischemia within 8 weeks prior to registration. * No history of cerebrovascular accident or transient ischemic attacks within the past 6 months from registration. * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for at least 6 months after completion of study therapy. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. * Women should not be lactating and, if of childbearing age, should have a negative pregnancy test (b-HCG test; serum or urine, minimum sensitivity 25 IU/L or equivalent units of b-HCG) within two weeks of registration in the study. Exclusion Criteria: * Patients who have had systemic therapy for melanoma or radiotherapy within 3 weeks prior to registering on the study or those who have not recovered from adverse events due to agents administered more than 3 weeks earlier. Patients with a history of endocrinopathies (e.g. hypothyroidism) are eligible if they are stable on hormone replacement therapy. Patients with a history of adrenal insufficiency are not eligible. * Patients may not be receiving any other investigational agents. * Patients with active brain metastasis are excluded * Patients with clinically significant cardiovascular or cerebrovascular disease * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit compliance with study requirements. * Patients who have other current malignancies are not eligible. Patients with other malignancies are eligible if they have been continuously disease free for \> 2 years prior to the time of registration. Patients with prior history at any time of any in situ cancer, lobular carcinoma of the breast in situ, cervical cancer in situ, atypical melanocytic hyperplasia or melanoma in situ are eligible. Patients with prior history of basal or squamous skin cancer are eligible. Patients who have had multiple primary melanomas are eligible. * Patients must not have autoimmune disorders or conditions of immunosuppression that require current ongoing treatment with systemic corticosteroids (or other systemic immunosuppressants), including oral steroids (i.e., prednisone, dexamethasone) or continuous use of topical steroid creams or ointments or ophthalmologic steroids or steroid inhalers. If a patient had been taking steroids, at least 2 weeks must have passed since the last dose.