Los Tres Paso: Neoadjuvant Palbociclib Monotherapy, Concurrent Chemoradiation Therapy, Adjuvant Palbociclib Monotherapy in Patients With p16INK4a Negative, HPV-Unrelated Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: * Larynx SCC, hypopharynx SCC, or oral cavity SCC. HPV-unrelated OPSCC \[defined as p16INK4a negative by IHC (staining in \< 70% of cells) or HPV High Risk (Type 16 or 18) negative by ISH\]. P16INK4a positive larynx SCC, hypopharynx SCC, and oral cavity SCC are eligible given the unknown effect of this on the biology of SCC of these subsites. * Overall Stage III, IVA, or IVB disease per AJCC version 7.0 * Measurable disease defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 10 mm with CT scan, as ≥ 20 mm by chest x-ray, or ≥ 10 mm with calipers by clinical exam. * At least 18 years of age. * Normal bone marrow function as defined below: * Absolute neutrophil count ≥ 1,000/mcL * Platelets ≥ 100,000/mcL * Hemoglobin ≥ 9.0 g/dL * QTc \< 500 msec by Fridericia * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry, for the duration of study participation, and for 90 days after completion of treatment. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. * Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable). Additional Cohort 1 Eligibility Criteria: Patients enrolling to Cohort 1 must meet…