This phase II trial studies the effect of cemiplimab in combination with low-dose paclitaxel and carboplatin in treating patients with squamous cell carcinoma of the head and neck that has come back (recurrent) or spread to other places in the body (metastatic). Immunotherapy with monoclonal antibodies, such as cemiplimab , may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Chemotherapy drugs, like paclitaxel and carboplatin, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving cemiplimab in combination with paclitaxel and carboplatin may work better in treating recurrent or metastatic squamous cell carcinoma of the head and neck.

PRIMARY OBJECTIVE:

I. To assess the overall response rate (ORR) at 12 weeks of treatment with the treatment combination cemiplimab, paclitaxel, and carboplatin.

SECONDARY OBJECTIVES:

I. To assess toxicity/tolerance to the proposed treatment combination (a safety run-in phase of ten patients will be performed initially).

II. To assess progression-free survival (PFS) and overall survival (OS) at one and two years.

EXPLORATORY OBJECTIVES:

I. Prospectively test the ability of our clinical nomogram to predict median OS in squamous cell carcinoma of the head and neck (SCCHN) patients planning to receive first-line cemiplimab in combination with low-dose weekly paclitaxel and carboplatin.

II. To assess the PFS and OS of patients with combined positive score (CPS) <1%, >1%, and > 20%.

III. Compare the predictive power of our nomogram to that of CPS in the prospective cohort, as well as evaluate the combined correlation of nomogram and CPS to median OS.

IV. Perform comprehensive immune analysis including phenotypic analysis of immune cell subsets using high dimensional spectral flow cytometry. T cell functionality and ability to produce cytokines after ex vivo stimulation for all T cells and E6/E7-reactive T cells (P16+ subset patients) and TCR sequencing to determine if clonal T cell populations emerge from the tumor of responding patients in comparison with non-responders.

OUTLINE:

Patients receive cemiplimab intravenously (IV) over 30 minutes every 3 weeks (Q3W) for up to 104 weeks, and paclitaxel IV over 60 minutes and carboplatin IV over 30 minutes once weekly (QW) for up to 24 weeks. Treatment continuous in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up at 14 days and then every 12 weeks.

Inclusion Criteria:

• Recurrent/metastatic (R/M) SCCHN of the oral cavity, oropharynx, larynx and hypopharynx
• No prior systemic therapy for treatment of R/M disease
• Patients with squamous cell carcinoma of an unknown primary are eligible provided their tumor tested positive for p-16 and they have previously received treatment for locoregional head and neck cancer
• Must be at least four weeks since prior radiation and/or surgery
• Must be at least four weeks from curative intent systemic therapy. Of note: patients who have received up to two courses of chemoradiotherapy (CRT) for locoregionally advanced disease are eligible. Induction chemotherapy will not be considered a separate line of therapy
• At least one measurable lesion as defined by Response Evaluation Criteria In Solid Tumors (RECIST) v1.1 on screening computed tomography (CT) or magnetic resonance imaging (MRI)
• 18 years of age and older
• Eastern Cooperative Oncology Group (ECOG) performance status 0-1
• White blood cell (WBC) count > 2,500 cells/uL
• Absolute neutrophil count (ANC) >1,500 cells/uL
• Platelet count >= 100,000 cells/uL
• Hemoglobin >= 9 g/dL
• Creatinine =< 1.6 mg/dL
• Total bilirubin =< 1.6 mg/dL
• Serum glutamic oxaloacetic transaminase (SGOT) (aspartate transaminase [AST]), serum glutamic-pyruvic transaminase (SGPT) (alanine aminotransferase [ALT]) =< 2.5 x upper limit of normal (ULN)
• Potassium >= lower limit of normal (LLN)
• Willingness to use medically acceptable contraception throughout the study period and four months after the final administration of treatment
• For female subjects with reproductive potential: a negative serum pregnancy test at baseline
• Ability and willingness to provide written informed consent and to comply with the study visits and assessment schedule

Exclusion Criteria:

• Disease amenable to curative local therapy
• Nasopharyngeal, salivary gland, lip, or sinonasal carcinoma
• Disease that requires corticosteroids or other ongoing immunosuppressive treatment
• Previous treatment with mAb-based immunotherapy for treatment of prior oncologic treatment
• Previous treatment with PI3K inhibitors
• Known brain metastases, unless stable for at least 21 days prior to registration
• Known infection human immunodeficiency virus (HIV), hepatitis B or C
• Clinically significant cardiac disease (e.g., congestive heart failure, unstable or uncontrolled angina, myocardial infarction) within the past six months
• History of pneumonitis within the past five years
• Recipient of live vaccines (including attenuated) within 30 days of planned study treatment
• Female patients who are pregnant or breast-feeding
• Any other condition or circumstance that could interfere with adherence to the study's procedures or requirements or otherwise compromise the study's objectives in the opinion of the Principal Investigator