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