Cemiplimab, Low-Dose Paclitaxel and Carboplatin for the Treatment of Recurrent/Metastatic Squamous Cell Carcinoma of the Head and Neck

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