A Phase II Study of the Interleukin-6 Receptor Inhibitor Tocilizumab in Combination With Ipilimumab and Nivolumab in Patients With Unresectable Stage III or Stage IV Melanoma

Inclusion Criteria: * Patients must have signed and dated an Institutional Review Board (IRB)/Independent Ethics Committee (IEC)-approved written informed consent form (ICF) in accordance with regulatory and institutional guidelines. This must be obtained before the performance of any protocol-related procedures that are not part of normal patient care. * Patients must be willing and able to comply with scheduled visits, treatment schedule, laboratory tests, tumor biopsies, and other requirements of the study. * All patients must be either Stage IIIb/c/d or Stage IV melanoma according to the American Joint Committee on Cancer (AJCC) (8th edition) and have histologically-confirmed melanoma that is felt to be surgically unresectable in order to be eligible. Please refer to the AJCC 8th edition Cancer Staging Manual for a description of tumor, lymph node, metastasis, and staging. * All melanomas, except ocular/uveal melanoma, regardless of primary site of disease will be allowed; mucosal melanomas are eligible. * Patients must not have received prior anticancer treatment for metastatic disease (for example, but not limited to, systemic, local, radiation, radiopharmaceutical). * Exceptions: Surgery for melanoma and/or post-resection brain radiotherapy (RT) if Central Nervous System (CNS) metastases and adjuvant RT for locoregional disease after resection and/or prior treatment with adjuvant IFN-alpha, ipilimumab or nivolumab (as described in Exclusion Criterion 2). * All patients must have their disease status documented by a complete physical examination and imaging studies within 4 weeks prior to the first dose of study drug. Imaging studies must include computerized tomography (CT) scan of chest, abdomen, pelvis, and all known sites of resected disease in the setting of Stage IIIb/c/d or Stage IV disease, and brain magnetic resonance imaging (\[MRI\]; brain CT is allowable if MRI is contraindicated). * The complete set of baseline radiographic images must be available before treatment initiation. * Eastern Cooperative Oncology Group (ECOG) performance status score of 0 or 1. * Tumor tissue from the resected site of disease must be provided for biomarker analyses * Prior treated CNS metastases must be without MRI evidence of recurrence for at least 4 weeks after treatment. Patients must be off immunosuppressive doses of systemic steroids (10 mg/day prednisone or equivalent) for at least 14 days prior to study drug administration, and must have returned to neurologic baseline status postoperatively. * The 4-week period of stability is measured after the completion of the neurologic interventions (i.e., surgery and/or radiation). * In addition to neurosurgery to treat CNS metastases, adjuvant radiation after the resection of CNS metastasis is allowed. Immunosuppressive doses of systemic steroids (doses \> 10 mg/day prednisone or equivalent) must be discontinued at least 14 days before study drug administration. * Prior surgery that required general anesthesia must be completed at least 4 weeks before study drug administration. Surgery requiring local/epidural anesthesia must be completed at least 72 hours before study drug administration. * Normal labs * Patient Re-enrollment: This study permits the re-enrollment of a patient that has discontinued the study as a screen failure (i.e., patient has not been dosed/has not been treated). If re-enrolled, the patient must be re-consented and satisfy all eligibility criteria. * Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[human chorionic gonadotropin (hCG)\] hormone) within 24 hours prior to the start of study drug. * Women of childbearing potential must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug(s) plus 5 half-lives of study drug plus 30 days (duration of ovulatory cycle). The half-life of nivolumab and ipilimumab is up to 25 days and 18 days, respectively. WOCBP should therefore use an adequate method to avoid pregnancy for a total of 23 weeks post treatment completion (Section 4.5). * Males who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug(s) plus 5 half lives of the study drug (s) plus 90 days (duration of sperm turnover). The half lives of nivolumab and ipilimumab are up to 25 days and 18 days, respectively. Men should therefore use an adequate method of contraception for a total of 31 weeks post treatment completion (Section 4.5). * Azoospermic males and WOCBP who are continuously not heterosexually active are exempt from contraceptive requirements. However, they must still undergo pregnancy testing as described in this section. Exclusion Criteria: * Patients with carcinomatosis meningitis or a history of current ocular/uveal melanoma are excluded. * Patients with previous nonmelanoma malignancies are excluded unless a complete resection or remission was achieved at least 2 years prior to study entry and no additional therapy is required or anticipated to be required during the study period (exceptions include, but are not limited to, nonmelanoma skin cancers, in situ bladder cancer, in situ gastric cancer or gastrointestinal stromal tumor, in situ colon cancers, in situ cervical cancers/dysplasia, or breast carcinoma in situ). * Patients with active, known, or suspected autoimmune disease. Patients with type I diabetes mellitus, residual hypothyroidism due to autoimmune thyroiditis only requiring hormone replacement, or skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment are permitted to enroll. For any cases of uncertainty, it is recommended that the Principal Investigator be consulted prior to signing informed consent. * Patients with a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone or equivalent) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids are permitted in the absence of active autoimmune disease. * Prior therapy for melanoma with the following exceptions which are allowed: 1) surgery for the melanoma lesion(s), 2) adjuvant RT after neurosurgical resection for CNS lesions or for resected locoregional disease, and 3) prior adjuvant interferon (IFN)-alpha, ipilimumab and nivolumab (see qualifier below). * Prior treatment with adjuvant IFN-alpha, adjuvant ipilimumab and/or nivolumab are allowed if completed 6 months prior to treatment. * Treatment directed against the melanoma (eg, chemotherapy, targeted agents, biotherapy, limb perfusion) that is administered after a prior complete resection other than adjuvant radiation after neurosurgical resection or resection of locoregional disease and IFN-alpha, ipilimumab and nivolumab for resected melanoma. * abnormalities labs * Corrected QT interval using Fridericia's formula value \> 480 msec at screening; family or personal history of long corrected QT interval (QTc) syndrome or ventricular arrhythmias including ventricular bigeminy at screening; previous history of drug induced QTc prolongation or the need for treatment with medications known or suspected of producing prolonged QTc intervals on electrocardiogram (ECG). * Congestive heart failure (New York Heart Association Class III or IV), myocardial infarction * Any serious or uncontrolled medical disorder or active infection