This study is being done to better understand whether or not cemiplimab by itself and in combination with other treatments given prior to surgery will cause your tumor to respond in a beneficial way; whether the drug(s) are safe and what side effects they cause; and other details about how they function in the body. One of the treatments that will be combined cemiplimab is another experimental drug called fianlimab. In this form, cemiplimab and fianlimab will each individually be called "study drug" or "study drugs" when combined.

Cemiplimab (also known as REGN2810) and fianlimab (also known as REGN3767) are both a type of drug called a monoclonal antibody. Antibodies are proteins naturally found in your blood that fight infections. A monoclonal antibody is a special kind of antibody that is manufactured as a medication to target specific proteins in the body that may be involved in your cancer.

• Cemiplimab is a drug that blocks the programmed death receptor 1 (PD-1), a cell receptor on immune cells
• Fianlimab is a drug that blocks the action of a protein called lymphocyte activation gene (LAG)-33 (LAG-3)

Key Inclusion Criteria:

• Patient must have a known diagnosis of NSCLC, HCC, or HNSCC as defined in the protocol
• Patient must be willing and able to provide blood samples at the indicated time points
• Patient must be willing and able to have excisional or core needle biopsies of tumor prior to initiation of cemiplimab as defined in the protocol
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
• Patient is determined to be a surgical candidate for resection of their tumor
• Adequate organ and bone marrow function as defined in the protocol

Key Exclusion Criteria:

• Patients who have had any systemic anti-cancer therapy or radiotherapy within 6 months prior to entering the study for their current tumor or a different primary tumor
• Patients whose tumor burden, or pace of tumor growth, in the opinion of the Investigator will not permit delaying surgery
• Patients who have participated in a study of an investigational agent or an investigational device within 4 weeks of study therapy or 5 half-lives (whichever is longer)
• Patients who have had major surgery within 14 days prior to initiation of neoadjuvant Therapy
• Patients with metastatic disease for whom the intent of surgery would not be curative
• Uncontrolled, intercurrent illness as defined in the protocol and as determined by the Investigator
• Is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study treatment
• Has active autoimmune disease that has required systemic treatment in the past 1 year
• Has a known, additional malignancy that is progressing and/or requires active treatment. Exceptions include patients with: basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy; in situ cervical or anal cancer; prostate cancer on stable dose of hormonal therapy without rising prostate-specific antigen (PSA); breast cancer who have been treated with curative intent, who may be on hormonal therapy.
• Encephalitis, meningitis, or uncontrolled seizures in the year prior to informed consent
• History of interstitial lung disease (eg, idiopathic pulmonary fibrosis, organizing pneumonia) or active, noninfectious pneumonitis that required immune-suppressive doses of glucocorticoids to assist with management. A history of radiation pneumonitis in the radiation field is permitted as long as pneumonitis resolved ≥6 months prior to study treatment.
• Uncontrolled infection with human immunodeficiency virus (HIV), HBV or hepatitis C infection (HCV); or diagnosis of immunodeficiency as defined in the protocol
• NSCLC cohorts only: Patients do not have a history of smoking. History of smoking is defined as smoking ≥100 cigarettes in a lifetime.
• NSCLC cohorts only: Patients with tumors tested positive for epidermal growth factor receptor (EGFR) gene mutations, anaplastic lymphoma kinase (ALK) gene translocations, or c-ros oncogene 1 (ROS1) fusions.

Note: Other protocol defined Inclusion/Exclusion criteria apply

All Individual Patient Data (IPD) that underlie publicly available results will be considered for sharing

Individual anonymized participant data will be considered for sharing once the indication has been approved by a regulatory body, if there is legal authority to share the data and there is not a reasonable likelihood of participant re-identification.

Qualified researchers may request access to anonymized patient level data or aggregate study data when Regeneron has received marketing authorization from major health authorities (e.g., FDA, European Medicines Agency (EMA), Pharmaceuticals and Medical Devices Agency (PMDA), etc) for the product and indication, has the legal authority to share the data, and has made the study results publicly available (eg, scientific publication, scientific conference, clinical trial registry).

Cohorts B and C are not randomized