The goal of this clinical research study is to find out if taking axitinib with ipilimumab is effective in treating advanced melanoma.

The safety and tolerability of the combination of ipilimumab and axitinib will be tested in advanced melanoma patients who are intolerable/refractory to anti-PD-1/PD-L1 therapy and have not previously received treatment with ipilimumab.

Inclusion Criteria:

• Diagnosis of advanced/unresectable melanoma - uveal melanoma is excluded
• Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2
• Adequate bone marrow, organ function and laboratory parameters as defined in protocol.
• Patients must have adequately controlled blood pressure (<150 systolic and <100 diastolic)
• At least 1 measurable lesion - per irRECIST 1.1 criteria
• Documented disease refractory or intolerant to anti-PD-1/PD-L1 inhibitor treatment: in the metastatic setting or in the adjuvant setting if relapse on or within 6 months from end of anti-PD-1 treatment
• If BRAFV600-mutant melanoma, patients may have had prior BRAF/MEK inhibitor therapy, or intolerance to these drugs
• No limit to prior lines of treatment but prior ipilimumab not permitted
• Prior treatment-related toxicity resolved to ≤ Grade 2 or baseline
• Participants with a prior or concurrent malignancy whose natural history or treatment (in the opinion of the treating physician) does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial.
• Prior to first dose of study treatment, patients must be at least 2 weeks from any prior major surgery.
• Able to undergo a pre-treatment and on-treatment tumor biopsy
• Female participants of childbearing potential must have a negative serum or urine β-HCG test result. Female participants of childbearing potential and male participants must agree to use methods of contraception that are highly effective. Pregnant or breast-feeding patients are not permitted to enroll.
• Patients with brain metastases are permitted assuming that the brain metastases have been adequately treated previously. Patients with uncontrolled or symptomatic brain metastases or leptomeningeal carcinomatosis that are not stable or require corticosteroids are not permitted,
• Active autoimmune disease requiring disease-modifying therapy at the time of screening is not permitted. Replacement therapy (e.g., physiologic corticosteroid therapy) is allowed
• Participants with known human immunodeficiency virus (HIV)-infection are eligible providing they are on effective anti-retroviral therapy and have undetectable viral load at their most recent viral load test and within 90 days prior to screening. Participants with a known history of hepatitis C virus (HCV) infection must have been treated and cured. Participants with HCV infection who are currently on treatment must have an undetectable HCV viral load prior to study start.

Exclusion Criteria:

• In patients with known liver cirrhosis, those with severe (Child Pugh C) hepatic impairment are excluded.
• Patients with Grade ≥3 hemorrhage within 4 weeks are excluded
• Patients with severe/unstable angina or symptomatic congestive heart failure within last 6 months are excluded
• Patients with cerebrovascular accident, transient ischemic attack within last 6 months are excluded.
• Patients with current use or anticipated need for treatment with drugs or foods that are known strong CYP3A4/5 inhibitors or strong CYP3A4/5 inducers, including their administration within 10 days prior to treatment start, are excluded.