This is a prospective, multi-center, open-label, non-randomized, multi-arm phase II trial to evaluate the efficacy of combination therapy with pembrolizumab and cetuximab for patients with recurrent/metastatic HNSCC. There will be four patient cohorts, including a PD-1/PD-L1 inhibitor-naïve, cetuximab-naïve arm (Cohort 1), a PD-1/PD-L1 inhibitor-refractory, cetuximab-naïve arm (Cohort 2), a PD-1/PD-L1 inhibitor-refractory, cetuximab-refractory arm (Cohort 3), and a cutaneous HNSCC arm (Cohort 4). A total of 83 patients (33 in Cohort 1, 25 in Cohort 2, 15 in Cohort 3, and 10 in Cohort 4) will be eligible to enroll. Patients will be enrolled at 4 sites: UC San Diego Moores Cancer Center, UC Los Angeles Jonsson Comprehensive Cancer Center, University of Michigan Comprehensive Cancer Center, and University of Washington Siteman Cancer Center.

Primary Objectives:

To determine the clinical efficacy of pembrolizumab combined with cetuximab for patients with R/M HNSCC.

1. Cohort 1 (PD-1/PD-L1 inhibitor-naïve, cetuximab-naïve): clinical efficacy defined as overall response rate.
2. Cohort 2 (PD-1/PD-L1 inhibitor-refractory, cetuximab-naïve): clinical efficacy defined as overall response rate.
3. Cohort 3 (PD-1/PD-L1 inhibitor-refractory, cetuximab-refractory): clinical efficacy defined as overall response rate.
4. Cohort 4 (cutaneous HNSCC): clinical efficacy defined as overall response rate.

Secondary Objectives:

1. To determine 12 month progression-free survival probability.
2. To determine overall survival.
3. To determine duration of response.
4. To assess safety and tolerability of pembrolizumab combined with cetuximab.
5. To evaluate the correlation between molecular markers and disease outcome.

Inclusion Criteria:

Patients must meet all of the inclusion criteria to participate in this study.

1. Ability to understand and the willingness to sign a written informed consent.
2. Histologically or cytologically proven squamous cell carcinoma of the head and neck (lip, oral cavity, oropharynx, larynx, hypopharynx, non-EBV related nasopharynx, sinonasal, cutaneous), not amenable to curative intent therapy.
3. Platinum-refractory disease, or ineligible/unfit for platinum-based therapy
4. Patients must have at least one measurable site of disease as defined by RECIST v.1.1, determined by investigator review
5. Age ≥ 18 years.
6. Eastern Cooperative Oncology Group (ECOG) Performance status 0 or 1.
7. Patient has adequate hematologic, hepatic and renal function
8. Female patient of childbearing potential has a negative serum or urine pregnancy within 72 hours prior to receiving the first dose of study medication.
9. Female patient of childbearing potential agrees to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication.
10. Male patient with a partner of childbearing potential agrees to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy.

Additional Inclusion Criterion for Cohort 1 (PD-1/PD-L1 Inhibitor-naïve, Cetuximab-naïve) and Cohort 2 (PD-1/PD-L1 Inhibitor-refractory, Cetuximab-naïve):

1. Cetuximab-naïve patients may not have received cetuximab therapy in the recurrent/metastatic setting (treatment in curative setting permitted)

Additional Inclusion Criterion for Cohorts 2 and 3 (PD-1/PD-L1 Inhibitor-refractory):

1. PD-1/PD-L1 inhibitor-refractory patients must have documented disease progression after prior response to anti-PD-1/PD-L1 therapy (response defined as stable disease, partial or complete response)

Additional Inclusion Criterion for Cohort 4 (Cutaneous HNSCC):

1. Cutaneous HNSCC must not be amenable to local treatment modalities, including surgery and/or radiation.

Exclusion Criteria:

Patients meeting any of the exclusion criteria at baseline will be excluded from study participation.

1. Patient has salivary gland primary.

2. Patient is currently receiving or has received another investigational agent within 4 weeks prior to Day 1 of study.

3. Patient has received chemotherapy or radiotherapy within 4 weeks prior to Day 1 of study. Prior palliative radiotherapy to metastatic lesion(s) is permitted, provided there is at least one measurable lesion that has not been radiated.

4. Patient has received a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or baseline) from adverse events due to a previously administered agents.

5. Patient has had major surgery or insufficient recovery from surgical-related trauma or wound healing within 14 days of Study Day 1.

6. Patient has had a prior Grade ≥ 3 immune-related adverse event (irAE) while receiving any previous immunotherapy agent, or any unresolved irAE > Grade 1.

7. Patient has had prior Grade 4 infusion reaction to cetuximab.

8. Patient has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer.

9. Patient has known active central nervous system (CNS) metastases and/or carcinomatous meningitis.

   Note: Patients with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability.

10. Patient has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs).

    Notes:

    • Patients with vitiligo, Grave's disease, or psoriasis not requiring systemic treatment within the past 2 years are not excluded.
    • Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment.

11. Patient has a diagnosis of immunodeficiency or is receiving systemic steroid therapy (>10mg prednisone daily, or steroid equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of pembrolizumab.

12. Patient has a known history of active TB (Baccillus Tuberculosis).

13. Patient has a known history of, or any evidence of active, non-infectious pneumonitis.

14. Patient has a known history of chronic interstitial lung disease.

15. Patient has an active infection requiring systemic therapy.

16. Patient has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator.

17. Patient has a known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.

18. Patient is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial.

19. Patient has known active Hepatitis B infection (defined as presence of HepB sAg and/ or Hep B DNA), active hepatitis C infection (defined as presence of Hep C RNA) and/or known Human Immunodeficiency Virus (HIV) carrier (HIV 1/2 antibodies).

20. Patient has received a live vaccine within 30 days of study Day 1.

Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed.

Additional Exclusion Criterion for Cohorts 1 (PD-1/PD-L1 inhibitor-naïve, cetuximab-naïve) and 4 (cutaneous):

1. Patient has received any prior immunotherapy with inhibitors of PD-1 or PD-L1.