NT219 Combined With Standard of Care Biologic Therapy in Recurrent/Metastatic Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: * 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. Exclusion Criteria: * Unknown origin squamous cancer. * EBV-driven NPC. * 4 lines or more in the relapsed/metastatic setting. * Pregnant or lactating, as the effects of NT219 on a fetus or child are unknown. Patients who are capable of childbearing or have partners capable of childbearing must use two forms of birth control including a barrier method to avoid pregnancy. * Known central nervous system metastases unless previously treated and clinically stable for at least one month. * Major surgery within 4 weeks or minor surgery within 1 week of starting therapy. * Known active HIV infection, unless treated with no detectable virus, or active HIV infection based on screening testing. * Participants with chronic hepatitis B virus (HBV) infection with active disease that meets the criteria for anti-HBV therapy and are not on suppressive antiviral therapy for at least 4 weeks prior to the first dose of study treatment. * Patients with known hepatitis C virus (HCV) who have not completed curative antiviral treatment at least 4 weeks prior to first dose of study treatment or have an HCV viral load above the limit of quantification at screening. * Prior anti-cancer biologic agent within 4 weeks prior to Study Day 1, or prior chemotherapy, targeted small molecular therapy, or radiation therapy within 2 weeks prior to Study Day 1, as wash-out considerations. * Vaccine administration within 4 weeks before the first dose of NT219 * Serious systemic infection within 4 weeks of the first dose of the study treatment, or clinically significant infection requiring hospitalization and/or IV anti-infective therapy within 2 weeks of the first dose of the study treatment. * Receipt of any organ transplantation including autologous and allogeneic stem cell transplantation, with the exception of transplants that do not require immunosuppression. * Diagnosed and/or treated for any other additional malignancy within 2 years of the first dose of study treatment with the exception of curatively treated basal cell or squamous cell carcinoma of the skin and curatively resected in situ cancers. Other exceptions may be considered with the PI's consultation. * Cohort 1: In addition to the general exclusion criteria, patients with active autoimmune disease requiring systemic treatment in the past two years with use of disease modifying agents, corticosteroids, or immunosuppressive drugs. Replacement therapy such as thyroxine, insulin, or physiologic corticosteroids is allowed. Well-managed or inactive autoimmune disorders, such as Hashimoto's thyroiditis, are allowed at the discretion of the PI. * Cohort 1: Any condition requiring systemic treatment with \>10mg prednisone or equivalent corticosteroid daily or other systemic immunosuppressive medication within 2 weeks of the first dose of study treatment. Topical, intranasal, intrabronchial, and ocular steroids are allowed. Steroids used as premedication for allergic reactions or as prophylactic management of AEs related to the study drugs specific in this protocol are allowed. * Cohort 2: Any of the following within 6 months of starting study treatment: ST elevation myocardial infarction, severe or unstable angina, uncontrolled cardiac ventricular arrhythmia, coronary or peripheral artery bypass graph or stent, cerebrovascular accident or stroke, or severe/uncontrolled congestive heart failure. Deep vein thrombosis that are hemodynamically stable do not exclude enrollment if the patient has been on a stable dose of anticoagulant for at least three months.