• Signed Written Informed Consent

‣ 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.

⁃ Subjects must be willing and able to comply with scheduled visits, treatment schedule, laboratory tests, and other requirements of the study.

• Type of Participant and Target Disease Characteristics

‣ Eastern Cooperative Oncology Group (ECOG) Performance Status 0-1.

⁃ 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.)

• Laboratory Testing Requirements

• Screening laboratory values obtained within -28 +/- 3 days of first dose must meet the following criteria:

⁃ White Blood Cells greater than or equal to 2000/μL

⁃ Neutrophils greater than or equal to 1500/μL

⁃ Platelets greater than or equal to 100 x 10³/μL

⁃ Hemoglobin greater than or equal to 9.0 g/dL

⁃ 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)

⁃ 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

⁃ 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)

• Reproductive Status

‣ 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).

⁃ Women must not be breastfeeding.

⁃ 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.

⁃ 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.

⁃ Azoospermic males and those who are continuously not heterosexually active are exempt from contraceptive requirements.

⁃ WOCBP who are continuously not heterosexually active are exempt from contraceptive requirements, however they must still undergo pregnancy testing as described in this section.