Palbociclib With Cetuximab and IMRT for Locally Advanced Squamous Cell Carcinoma

Inclusion Criteria: 1. Locally advanced histology or cytology proven squamous cell carcinoma of oral cavity, oropharynx, larynx, and hypopharynx. 2. Locally advanced SCCCH patients who would be considered for concurrent cetuximab and IMRT as a definitive treatment. 3. Age ≥ 18 yeas old. 4. Available tissue to determine HPV status and the other biomarkers of interest. 5. ECOG status ≤ 1. 6. Adequate bone marrow, liver, and renal functions, defined as: * Platelet count ≥150 x 109/L, Absolute Neutrophile Count (ANC) ≥1.5 x 109/L, Hgb ≥9 gm/dL * ALT and AST ≤ 1.5 upper limit normal (ULN); serum total bilirubin ≤ ULN * Serum creatinine ≤ 1.5 x ULN, or calculated or measured creatinine clearance (by Cockcroft-Gault Equation) ≥ 50 mL/min * Magnesium ≥ the lower limit of normal 7. Women of childbearing potential must have a negative pregnancy test performed within 7 days prior to the start of study drug. 8. Male and female subjects of child-bearing potential must agree to use double-barrier contraceptive measures, oral contraception, or avoidance of intercourse during the study and for 6 months after last investigational drug dose received. 9. Subject or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure. Exclusion Criteria: Potential subjects who meet ANY of the following exclusion criteria are not eligible for enrollment into this study: 1. SCCHN patients with distance metastasis. 2. Major surgery \< 4 weeks or minor surgery \< 2 weeks prior to the first day of study treatment. 3. Patients with previous chemotherapy for cancer treatment and radiation to the head and neck areas. 4. Patients who were previously treated with any CDK4/6 inhibitors or cetuximab. 5. SCCHN with expressed p16 by IHC (only in expansion cohort). 6. Active cardiac disease described as: * Left ventricular ejection fraction (LVEF) \< 50% by Multiple Grated acquisition (MUGA) scan or echocardiogram (ECHO). * QTc \> 480 msec on screening EKG (using the QTcF formula). * Congenital long QT syndrome * Myocardial infarction or active uncontrolled angina pectoris within the last 6 months prior to the first day of study treatment * Uncontrolled significant cardiac arrhythmias except for benign premature ventricular contractions (PVC) and premature atrial contractions (PAC). * Symptomatic pericarditis * History of cardiomyopathy 7. Weight loss more than 10% from baseline body weight before illness. 8. Active clinically serious infections or other serious uncontrolled medical conditions. 9. Substance abuse, medical, psychological or social conditions that may, in the opinion of the Investigator, interfere with the patient's participation in the study or evaluation of the study results. 10. Unable to swallow an intact palbociclib tablet. 11. Impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of palbociclib. 12. Known HBV, HCV, and/or HIV infection. 13. Patients who are currently treated with drugs known to be strong inhibitors or inducers of isoenzyme CYP3A, and the treatment cannot be discontinued or switched to a different medication prior to starting study drug. 14. Patients who have taken herbal medications and certain fruits within 7 days prior to starting study drug. Herbal medications include, but are not limited to St. John's wort, Kava, ephedra (ma huang), gingko biloba, dehydroepiandrosterone (DHEA), yohimbe, saw palmetto, and ginseng. Fruits include the CYP3A inhibitors Seville oranges, grapefruit, pomelos, or exotic citrus fruits.