Key Inclusion Criteria:

          -  At least 1 measurable lesion

          -  Eastern Cooperative Oncology Group (ECOG) performance status ≤1

          -  Adequate bone marrow function

          -  Adequate renal function

          -  Adequate hepatic function

          -  Archived or newly obtained tumor material

          -  Patients must consent to undergo biopsies of CSCC lesions (Groups 2, 4 and 6)

          -  Surgical or radiological treatment of lesions contraindicated

        Key Exclusion Criteria:

          -  Ongoing or recent (within 5 years) evidence of significant autoimmune disease that
             required treatment with systemic immunosuppressive treatments, which may suggest risk
             for immune-related adverse events

          -  Prior treatment with an agent that blocks the PD-1/PD-L1pathway

          -  Prior treatment with a BRAF inhibitor

          -  Prior treatment with other immune-modulating agents within fewer than 4 weeks prior to
             the first dose of cemiplimab, or associated with immune-mediated adverse events that
             were ≥ grade 1 within 90 days prior to the first dose of cemiplimab, or associated
             with toxicity that resulted in discontinuation of the immune-modulating agent.
             Examples of immune-modulating agents include therapeutic vaccines, cytokine
             treatments, or agents that target cytotoxic T-lymphocyte antigen 4 (CTLA-4), 4-1BB
             (CD137), or OX-40.

          -  Untreated brain metastasis(es) that may be considered active

          -  Immunosuppressive corticosteroid doses (>10 mg prednisone daily or equivalent) within
             4 weeks prior to the first dose of cemiplimab

          -  Infection with human immunodeficiency virus (HIV) and/or chronic/active infection with
             hepatitis B virus or hepatitis C virus

          -  History of non-infectious pneumonitis within the last 5 years

          -  Allergic reactions or acute hypersensitivity reaction attributed to antibody
             treatments

          -  Known allergy to doxycycline or tetracycline

          -  Patients with a history of solid organ transplant

          -  Any medical co-morbidity, physical examination finding, or metabolic dysfunction, or
             clinical laboratory abnormality that renders the patient unsuitable

        Other protocol-defined inclusion/exclusion criteria apply