Nivolumab Alone or Plus Relatlimab or Ipilimumab for Patients With Locally-Advanced Unresectable or Metastatic Basal Cell Carcinoma

Inclusion Criteria: 1. Signed Written Informed Consent 1. Subjects must have signed and dated an Institutional Review Board (IRB)-approved written informed consent form 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 subject care. 2. Subjects must be willing and able to comply with scheduled visits, treatment schedule, laboratory tests, and other requirements of the study. 2. Type of Participant and Target Disease Characteristics 1. Eastern Cooperative Oncology Group (ECOG) Performance Status 0-1. 2. Participants with histologically confirmed Basal Cell Carcinoma with disease that is considered by the investigator to be unresectable or metastatic. i) COHORT A: Patients with advanced BCC who are treatment-naïve (i.e., no prior hedgehog pathway inhibitors and T cell modulating agents) will receive anti-PD-1 (nivolumab) alone. ii) COHORT B: • Patients with advanced BCC who experience disease progression on anti-PD-1 (nivolumab) + anti-LAG-3 (relatlimab) will receive anti-PD-1 (nivolumab) + anti-CTLA-4 (ipilimumab). iii) COHORT C: • Patients with advanced BCC who experience disease progression on anti-PD-1 (on or off trial) will receive anti-PD-1 (nivolumab) + anti-LAG-3 (relatlimab). c. At least one measurable lesion by the RECIST 1.1 Criteria. d. Participants with Gorlin syndrome will be permitted to enroll in the study. e. Male or female, aged 18 years or older. f. Patients may not have received prior T cell modulating agents for BCC (e.g., anti-CTLA-4, anti-PD-L1, anti-LAG-3, anti-KIR, etc.) 3. Laboratory Testing Requirements Screening laboratory values obtained within -28 +/- 3 days of first dose must meet the following criteria: 1. White Blood Cells greater than or equal to 2000/μL 2. Neutrophils greater than or equal to 1500/μL 3. Platelets greater than or equal to 100 x 10³/μL 4. Hemoglobin greater than or equal to 9.0 g/dL 5. Serum creatinine less than or equal to 1.5 x Upper Limit of Normal (ULN)or creatinine clearance (CrCl) greater than or equal to 40 mL/minute (using Cockcroft/Gault formula) 6. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) less than or equal to 3 x ULN, except in patients with liver metastases whose values may be less than or equal to 5 x ULN 7. Total Bilirubin less than or equal to 1.5 x ULN (except subjects with Gilbert Syndrome who may have total bilirubin less than or equal to 3.0 mg/dL) 4. Reproductive Status 1. Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the initial administration of study drug, then every 4 weeks +/- 1 week thereafter for the duration of treatment with study drug(s). 2. Women must not be breastfeeding. 3. WOCBP must agree to follow instructions for method(s) of contraception from the time of enrollment for the duration of treatment with study drug(s) plus approximately 5 half-lives of study drug(s) plus 30 days (duration of ovulatory cycle) for a total of 5 months post treatment completion. 4. 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 approximately 5 half-lives of study drug(s) plus 90 days (duration of sperm turnover) for a total of 7 months post-treatment completion. 5. Azoospermic males and those who are continuously not heterosexually active are exempt from contraceptive requirements. 6. 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: 1. Medical Conditions 1. Pregnant or nursing women 2. Central nervous system metastases, unless stable for at least 4 weeks and no longer requiring steroid therapy. 3. Patients with an autoimmune disease or with a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalent) or other immunosuppressive medications may be permitted to enroll only after discussion with the study P.I. 4. Participants with human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS). 5. Viral hepatitis. i. Participants with active hepatitis B (positive hepatitis B surface antigen \[HBsAg\] or hepatitis C virus (HCV) (positive HCV RNA) are excluded. ii. Patients with past Hepatitis B virus (HBV) infection or resolved HBV infection (defined as the presence of hepatitis B core antibody \[HBcAb\] and the absence of HBsAg) are not ineligible, but HBV DNA quantification must be performed and results discussed with the P.I. iii. HBV carriers or those participants requiring antiviral therapy are not eligible to participate. iv. Patients positive for HCV antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV RNA after discussion with the study P.I. f. Participants with a prior malignancy active within the previous 2 years may be permitted to enroll only after discussion with the study P.I. Examples might include locally curable cancers that have been apparently cured, such as squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the prostate, cervix, or breast. g. Organ transplant recipients with a functioning allograft will be excluded from this study. h. For Cohorts B and C, patients may be excluded from the study if they previously experienced a toxicity to immunotherapy that, in the opinion of the investigator, would make it unsafe to restart therapy. Examples may include a Grade 3 or greater immune mediated adverse event that was considered related to previous immunotherapy and required immunosuppressive therapy, or an immune mediated adverse event that was considered related to previous immunotherapy and is still \> grade 1 despite administration of immunosuppressive therapy. Exceptions may include Grade 3 ophthalmologic immune-mediated events that improved to Grade 1 within 2 weeks after topical therapy only, or Grade 3 endocrine immune-mediated events that did not result in symptoms lasting \>6 weeks and are not requiring \>7.5mg prednisone or equivalent per day. i) For Cohort C, Troponin T (TnT) or I (TnI) \> 2 × institutional ULN. Participants with TnT or TnI levels between \> 1 to 2 × ULN will be permitted if a repeat levels within 24 hours are ≤ 1 ULN. If TnT or TnI levels are between \>1 to 2 × ULN within 24 hours, the participant may undergo a cardiac consultation and be considered for treatment, following cardiologist recommendation. When repeat levels within 24 hours are not available, a repeat test will be conducted as soon as possible. If TnT or TnI repeat levels beyond 24 hours are \< 2 × ULN, the participant may undergo a cardiac consultation and be considered for treatment, following cardiologist recommendation. 2. Allergies and Adverse Drug Reaction 1. History of severe allergy or hypersensitivity to study drug components. 2. Patients with a history of a severe toxicity to an immune checkpoint blocking drug may be permitted to enroll only after discussion with the study P.I. 3. Other Exclusion Criteria 1. Prisoners or participants who are incarcerated may be permitted to enroll only after discussion with the study P.I. 2. Participants who are detained for treatment of either a psychiatric or physical (e.g., infectious disease) illness.