Nivolumab Plus Relatlimab or Ipilimumab in Metastatic Melanoma Stratified by MHC-II Expression

Inclusion Criteria: * Signed and dated written informed consent. * ≥ 18 years of age at the time of informed consent. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Histologically confirmed locally advanced/unresectable or metastatic melanoma. * Patients who have received prior anti-CTLA-4 or anti-PD-1/PD-L1 for adjuvant treatment of melanoma are eligible if \> 6 months have elapsed between the last dose of adjuvant treatment and starting this study - provided there is no history of life-threatening toxicity related to such prior treatment, or such toxicity is unlikely to re-occur with standard countermeasures (e.g. hormone replacement after endocrinopathy). * Patients who have received adjuvant therapy with interferon and/or a BRAF inhibitor and/or MEK inhibitor for adjuvant therapy are permitted to enroll. * At least one measureable target lesion as defined by RECIST 1.1 which can be followed byCT or MRI. * If located in a previously irradiated area, a tumor lesion is considered a measurable/target lesion only if subsequent disease progression in the lesion has been documented at least 90 days following completion of radiotherapy. * Adequate organ and bone marrow function ≤ 14 days prior to first dose of protocol-indicated treatment: * White blood cell count (WBC) ≥ 2,000/mm3 * Absolute neutrophil count (ANC) ≥ 1,500/mm3 * Platelets ≥ 75,000/mm3 * Hemoglobin ≥ 8.0 g/dL. * Serum creatinine ≤ 2.0x upper limit of normal (ULN), or calculated creatinine clearance (CrCl) \> 40 mL/min per the Cockcroft-Gault formula (Appendix 1). * Total bilirubin ≤ 1.5x ULN (except patients with Gilbert Syndrome, who must have total bilirubin \< 3.0 mg/dL). * AST (aspartate aminotransferase) and ALT (alanine aminotransferase) ≤ 3.0x ULN (≤ 5.0x ULN in those with hepatic metastases) * Acceptable troponin level ≤ 14 days prior to first dose of protocol-indicated treatment: * Troponin T (TnT) or I (TnI) ≤ 2× institutional ULN. * Subjects with TnT or TnI levels between \>1 to 2× ULN will be permitted if repeat levels within 24 hours are ≤ 1x ULN. * If TnT or TnI levels are \>1 to 2× ULN within 24 hours, the subject may undergo a cardiac evaluation and be considered for treatment based on the discretion of the PI. * When repeat levels within 24 hours are not available, a repeat test should be conducted as soon as possible. * If TnT or TnI repeat levels beyond 24 hours are \< 2x ULN, the subject may undergo a cardiac evaluation and be considered for treatment, based on the discretion of the PI. * Arm A: Corrected QT interval (QTc) by Fridericia's method (QTcF) assessed by electrocardiogram (ECG) completed ≤ 28 days before initiation of protocol treatment • QTcF ≤ 480 msec * Tumor tissue from a biopsy or resection obtained since completion of the last systemic therapy must be available for analysis of MHC-II status and for biomarker analysis. If a sample is not available or if the quantity or quality of tissue is insufficient to provide adequate results, an additional biopsy may be performed for MHC-II analysis. Patients cannot be enrolled on the study unless MHC-II is known. * Women must not be breastfeeding * A woman of childbearing potential must have a negative serum pregnancy test within 14 days prior to receiving first dose of protocol-indicated treatment, and must agree to follow instructions for using acceptable contraception (Appendix 4) from the time of signing consent, and for 165 days (24 weeks) after her last dose of protocol-indicated treatment. * A man able to father children who is sexually active with a woman of childbearing potential must agree to follow instructions for using acceptable contraception from the time of signing consent, and for 225 days (33 weeks) after his last dose of protocol-indicated treatment. Exclusion Criteria: * Patients with uveal melanoma. * Prior systemic anticancer therapy for unresectable or metastatic melanoma. * Prior treatment with LAG-3 targeted agents. * Subjects with active, known, or suspected autoimmune disease. Subjects with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll. * Uncontrolled or significant cardiovascular disease including, but not limited to, any of the following: * Myocardial infarction (MI) or stroke/transient ischemic attack (TIA) within the 6 months prior to consent. * Uncontrolled angina within the 3 months prior to consent. * Any history of clinically significant arrhythmias (such as ventricular tachycardia, ventricular fibrillation, torsades de pointes, or poorly controlled atrial fibrillation). * QTc prolongation \> 480 msec. * History of other clinically significant cardiovascular disease (i.e., cardiomyopathy, congestive heart failure with New York Heart Association \[NYHA\] functional classification III-IV, pericarditis, significant pericardial effusion, significant coronary stent occlusion, poorly controlled deep venous thrombosis, etc). * Cardiovascular disease-related requirement for daily supplemental oxygen. * History of two or more myocardial infarctions OR two or more coronary revascularization procedures. * Subjects with history of myocarditis, regardless of etiology. * A confirmed history of encephalitis, meningitis, or uncontrolled seizures in the year prior to informed consent. * Participants with a condition requiring systemic treatment with either corticosteroids (\>10 mg daily prednisone or equivalent) or other immunosuppressive medications within 14 days of enrollment. Inhaled or topical steroids, and adrenal replacement steroid doses \>10 mg daily prednisone or equivalent, are permitted in the absence of active autoimmune disease. * Subjects with active central nervous system (CNS) metastases, active brain metastases or leptomeningeal metastatic foci. For the subjects with brain metastases, if they are asymptomatic, they are eligible to participate in this study. If participants have received treatment for brain metastases and have no clinical evidence of progressive disease at least 1 week after completion of treatment for brain metastases and within 28 days prior to the first dose of protocol-indicated treatment on this study, they are eligible to participate in this study. * Known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS). * Known history of hepatitis B or hepatitis C. * Any significant medical condition, laboratory abnormality, or psychiatric illness, that would prevent the subject from participating in the study or place the subject at unacceptable risk if he/she were to participate in the study, or any condition that confounds the ability to interpret data from the study. * Subjects with life expectancy \< 6 months. * Subjects receiving any other investigational or standard antineoplastic agents. * Prior malignancy active within the previous 3 years except for locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the prostate, cervix, or breast. * Prisoners or participants who are involuntarily incarcerated. * Participants who are compulsorily detained for treatment of either a psychiatric or physical (e.g. infectious disease) illness. * Psychological, familial, sociological, or geographical conditions that potentially hamper compliance with the study protocol and follow-up schedule; those conditions should be discussed with the participant before registration in the trial.