The purpose of the study is to find out if the study drugs Avelumab, Cetuximab, and Palbociclib will slow or stop your cancer from getting worse, and whether it causes side effects. The second purpose is to measure whether your cancer responds to the study drugs Avelumab, Cetuximab, and Palbociclib. The study drugs Avelumab, Cetuximab, and Palbociclib are types of drugs called a monoclonal antibody. Monoclonal antibodies are made to recognize, target, and bind to specific proteins on cells the building blocks making up your tissues.

This is an open-label phase I trial with a 3+3 dose escalation design. All patients will receive avelumab, cetuximab, and palbociclib. This study will enroll patients with head and neck squamous cell carcinoma not amenable to curative intent therapy.

Treatment will be administered in 28 day cycles with a pre-defined dose escalation schedule.

Inclusion Criteria:

• Histologically or cytologically proven squamous cell carcinoma of the head and neck not amenable to curative intent therapy.
• Presence of measurable tumor lesions per RECIST criteria v1.1
• Life expectancy greater than 12 weeks.
• Adequate hematologic, hepatic, and renal function
• Negative serum or urine pregnancy test for women of child bearing potential

Exclusion Criteria:

• Prior therapy with an EGFR inhibitor or PD-1 or PD-L1 inhibitor in the recurrent or metastatic setting
• Uncontrolled central nervous system metastases (stable metastases permitted)
• Chemotherapy 28 days prior to first administration of study treatment and/or monoclonal antibody ≤8 weeks prior to first administration of study treatment.
• History of other malignancies,
• Concurrent systemic immunosuppressant therapy (eg, cyclosporine A, tacrolimus, etc., or chronic administration of >10 mg/day of prednisone or equivalent)
• Prior organ transplantation
• Known history of human immunodeficiency virus (HIV) or active infection with hepatitis C virus (HCV) or hepatitis B virus (HBV).