Inclusion Criteria:

          -  Histologically or cytologically confirmed diagnosis of squamous cell carcinoma of the
             head and neck.

          -  Disease must be considered incurable. Incurable is defined as metastatic disease or a
             local or regional recurrence in a previously irradiated site that is unresectable (or
             patient declines resection).

          -  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. (Phase I only: patients without
             measurable disease by RECIST 1.1 criteria but with evaluable disease by imaging or
             physical exam will be eligible as well.)

          -  Phase I only: any (or no) prior therapy for metastatic disease is allowed, including
             cetuximab. If a patient has not received prior standard therapy, s/he must have been
             offered and refused prior standard therapy.

          -  Phase II only:

               -  Arm 1: disease progression after at least one cycle of prior treatment with
                  cisplatin or carboplatin for incurable disease. Prior treatment with cetuximab
                  for incurable disease is not permitted.

               -  Arms 2 and 3: disease progression after at least one cycle of treatment with
                  cetuximab for incurable disease.

          -  Phase II only: at least one line of prior therapy for incurable disease.

          -  Phase II only:

               -  Arms1 and 2: disease must be determined to be HPV-unrelated. HPV-unrelated SCCHN
                  is defined as either p16-negative OPSCC or non-OPSCC (larynx, hypopharynx, oral
                  cavity) or p16-negative unknown primary SCC presenting with a level 2 or 3 neck
                  node. p16 will be assessed by IHC; a specimen showing any staining will be
                  considered p16-positive.

               -  Arm 3: disease must be HPV-related SCCHN (defined as OPSCC or unknown primary
                  presenting with a neck mass that is either p16 positive or HPV ISH or PCR
                  positive).

          -  Minimum of 14 days elapsed since the end of any prior therapy.

          -  At least 18 years of age.

          -  Resolution of all acute toxic effects of prior anti-cancer therapy or surgical
             procedures to NCI CTCAE version 4.0 Grade ≤ 1 (except alopecia or other toxicities not
             considered a safety risk for the patient at investigator's discretion)

          -  ECOG performance status ≤ 2

          -  Adequate bone marrow and organ function as defined below:

               -  Absolute neutrophil count ≥ 1,500 mm3

               -  Platelets ≥ 100,000 mm3

               -  Hemoglobin > 9 g/dL

               -  Total bilirubin ≤ 1.5 x IULN except in the case of patients with Gilbert's
                  disease

               -  AST (SGOT) and ALT (SGPT) ≤ 2.5 x IULN for patients without liver metastases and
                  ≤ 5.0 x IULN for patients with liver metastases

               -  Alkaline phosphatase ≤ 2.5 x IULN for patients without bone metastases and ≤ 5.0
                  x IULN for patients with bone metastases

               -  Serum creatinine ≤ 1.5 x IULN OR calculated creatinine clearance ≥ 50 mL/min/1.73
                  m2 for patients with creatinine levels above institutional normal

          -  Baseline corrected QT interval (QTc) < 480 ms.

          -  Women of childbearing potential and men must agree to use adequate contraception
             (hormonal or barrier method of birth control, abstinence) prior to study entry and for
             the duration of study participation. Should a woman become pregnant or suspect she is
             pregnant while participating in this study, she must inform her treating physician
             immediately.

          -  Available archival tumor tissue for the proposed correlative studies.

          -  Ability to understand and willingness to sign an IRB approved written informed consent
             document (or that of legally authorized representative, if applicable).

        Exclusion Criteria:

          -  Phase II, Arm 1 only: prior treatment with cetuximab.

          -  Resolution of all acute toxic effects of prior anti-cancer therapy or surgical
             procedures to NCI CTCAE version 4.0 Grade ≤ 1 (except alopecia or other toxicities not
             considered a safety risk for the patient at investigator´s discretion)

          -  A history of other malignancy ≤ 1 year previous with the exception of basal cell or
             squamous cell carcinoma of the skin which were treated with local resection only,
             carcinoma in situ of the cervix, or synchronous H&N primaries.

          -  Currently receiving any other investigational agents.

          -  Patient must not have a history of or clinical evidence of central nervous system
             metastases or leptomeningeal carcinomatosis, except for individuals who have had
             previously-treated CNS metastases, are asymptomatic, and have had no requirement for
             steroids or anti-seizure medications (with the exception of Keppra) for 1 month prior
             to first dose of PD 0332991.

          -  A history of allergic reactions attributed to compounds of similar chemical or
             biologic composition to PD 0332991, cetuximab, or other agents used in the study.

          -  Treated within the last 7 days prior to Day 1 of protocol therapy with:

               -  Food or drugs that are known to be CYP3A4 inhibitors (e.g. grapefruit juice,
                  verapamil, ketoconazole, miconazole, itraconazole, erythromycin, clarithromycin,
                  telithromycin, indinavir, ritonavir, nelfinavir, atazanavir, amprenavir,
                  nefazodone, diltiazem, and delavirdine) or inducers (i.e. dexamethasone,
                  glucocorticoids, progesterone, rifampin, phenobarbital, St. John's wort).

               -  Drugs that are known to prolong the QT interval.

               -  Drugs that are proton pump inhibitors.

          -  Uncontrolled electrolyte disorders that can compound the effects of a QTc-prolonging
             drug (e.g., hypocalcemia, hypokalemia, hypomagnesemia)

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, or psychiatric illness/social situations that would limit compliance with
             study requirements.

          -  Pregnant and/or breastfeeding. Women of childbearing potential must have a negative
             serum pregnancy test within 28 days of study entry. Female patients must be surgically
             sterile or be postmenopausal, or must agree to use effective contraceptive during the
             period of the trial and for at least 90 days after completion of treatment. The
             decision of effective contraception will be based on the judgment of the principal
             investigator or a designated associate.

          -  Phase I and Arm 1 of Phase II: Known HIV-positivity and on combination antiretroviral
             therapy because of the potential for pharmacokinetic interactions with PD 0332991. In
             addition, these patients are at increased risk of lethal infections when treated with
             marrow-suppressive therapy. Appropriate studies will be undertaken in patients
             receiving combination antiretroviral therapy when indicated.

        Arms 2 and 3 of Phase II: patients with HIV infection and antiretroviral therapy are not
        excluded, as there are no pharmacokinetic tests being performed.