Phase II Trial Evaluating the Efficacy of Palbociclib in Combination With Carboplatin for the Treatment of Unresectable Recurrent or Metastatic Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: * Histologically documented progressive squamous cell head and neck cancer with or without metastases, not amenable to curative treatment; or the patient has documented refusal of curative treatment. * ECOG performance status of 0-2. Eastern Cooperative Oncology Group Performance Status: an attempt to quantify cancer patients' general well-being and activities of daily life. The score ranges from 0 to 5 where 0 is asymptomatic and 5 is death. * Presence of measurable disease by CT scan per RECIST v1.1. * Age ≥18 years. * Life expectancy of ≥12 weeks. * Women of childbearing potential must have a negative serum or urine pregnancy test at time of screening and confirmed within 3 days prior to treatment. Women not of child-bearing potential will be defined as all women older than age 50 and anovulatory for 12 months. * Signed and dated informed consent document indicating that the patient (or legally acceptable representative) has been informed of all pertinent aspects of the trial prior to enrollment. * Willingness and ability to comply with scheduled visits, treatment plans, laboratory tests, and other study procedures. * Adequate organ and marrow function Exclusion Criteria: * Previous treatment with cytotoxic chemotherapy therapy in the recurrent/metastatic setting. Previous treatment with non-cytotoxic agents in the recurrent/metastatic setting is permitted. Gastrointestinal abnormalities causing impaired absorption precluding administration of oral medications. * Evidence of untreated or progressive brain metastases, spinal cord compression, or carcinomatous meningitis. * A serious uncontrolled medical disorder or active infection that would impair their ability to receive study treatment. * Dementia or significantly altered mental status that would prohibit the understanding or rendering of informed consent and compliance with the requirements of this protocol. * Patients (male and female) having procreative potential who are not willing or not able to use adequate contraception. Women who are pregnant or breast-feeding. * Patients residing in prison. * Prior experimental therapy within 30 days of enrollment. * Availability of curative treatment option for the patient's cancer, whether surgery, chemotherapy, radiation, or combination thereof, unless the patient has documented refusal of curative treatment. * Current use or anticipated inability to avoid use of drugs that are known strong CYP3A4/5 inhibitors (atazanavir, boceprevir, conivaptan, clarithromycin, grapefruit or grapefruit juice, indinavir, itraconazole, ketoconazole, nelfinavir, nefazodone, posaconazole, ritonavir, saquinavir, telaprevir, telithromycin, voriconazole ). * Current use or anticipated inability to avoid use of drugs that are known strong CYP3A4/5 inducers (carbamazepine, dexamethasone, fosphenytoin, phenytoin, phenobarbital, rifabutin, rifampin, rifapentine, St. John's wort). * Patients with a history of severe allergic reaction to cisplatin or carboplatin