• Age 18 and over.

• ECOG PS 0-2.

• Incurable head and neck squamous cell carcinoma of mucosal origin (oral cavity, tongue, oropharynx, pharynx, larynx, sinonasal and non-EBV-driven NPC).

• Adequate organ and marrow function as defined by routine lab testing including calculated creatinine clearance \>60 mL/min, total bilirubin \< 1.5x the ULN, ALT and AST \<5x the ULN, ANC \>1500, and platelets \>100,000.

• Measurable disease by RECIST on CT (including a diagnostic CT performed as part of a PET-CT) or MRI available for review.

• Recovered from clinically significant adverse events of most recent anti-cancer therapy prior to enrollment.

• Cohort 1: In addition to the general inclusion criterion, patients with tumor tissue CPS \>1 for whom single agent pembrolizumab is appropriate OR who derived significant clinical benefit from anti-PD-1 therapy (as single agent or combination) in the first line setting. No more than 7 patients with each profile (PD-1 inhibitor naïve vs PD-1 inhibitor experienced with benefit) can be enrolled in the first stage of Cohort 1.

• o Significant clinical benefit is defined as treatment duration \>=6 months and/or PR/CR as best objective response prior to disease progression.

• Cohort 1: In addition to the above inclusion criterion, patients must have accessible sites of disease not involving target lesions that are amenable to sequential biopsies, and participants willing to undergo sequential tumor biopsies as long as the treating investigator considers to be clinically safe.

• Cohort 2: In addition to the general inclusion criteria, patients have had progression or recurrence in the relapsed/metastatic setting to PD-1 inhibitors given with or without cytotoxic chemotherapy without significant clinical benefit OR who are candidates for cetuximab monotherapy.

⁃ Significant clinical benefit is defined as treatment duration \>=6 months and/or PR/CR as best objective response prior to disease progression.