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