Targeting PD-1 Therapy Resistance With Focused High or High and Low Dose Radiation in SCCHN

Inclusion Criteria: * Pathologically confirmed squamous cell carcinoma of the head and neck with evidence of metastatic disease considered incurable by local therapies. Patients without pathologic or cytologic evidence of metastatic disease should have unequivocal evidence of metastasis from physical examination or radiologic evaluation. * Patients must have evidence of radiologic or clinical disease progression during previous treatment with systemic PD-1 directed therapy, or have stable disease on prior PD-1 therapy (at least 6 doses) and/or have been deemed not to derive clinical benefit from PD-1 directed treatment. * Patients must have least 3 measurable non-CNS based lesions that have not previously been irradiated. Palliative radiation must be potentially indicated for at least one of these lesions. * Patients must agree to undergo a research biopsy, if tumor is accessible, at baseline (mandatory) and at the end of cycle 2 of pembrolizumab (optional). . * Prior systemic therapy: Patients must be at least 2 weeks from prior chemotherapy, biological agents, immunotherapy or any investigational drug product, with adequate recovery of toxicity. For investigational agents, the minimum time from prior therapy is 5 half-lives if this is longer than 2 weeks in duration. * Prior radiation therapy: Patients must be at least 2 weeks from prior radiation therapy * Concurrent administration of other cancer specific therapy during the course of this study is not allowed. * Only patients 18 years and older are eligible. There is no upper age limit but the patients must be able to medically tolerate the regimen. Adverse event data are currently unavailable on the use immune checkpoint blockade for participants \< 18 years of age, and thus children are excluded from this study. * ECOG performance status \<=1 (see Appendix A). * Ability to understand and the willingness to sign a written informed consent document * Female subjects of childbearing potential must have a negative serum pregnancy test at screening. * Female and male subjects of childbearing potential must agree to use an adequate method of contraception as outlined in section 5.7.1. Contraception is required prior to study entry and for the duration of study participation and 4 months after completion of pembrolizumab administration. --Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. * Participants must have normal organ and marrow function as defined below: * leukocytes ≥3,000/mcl * absolute neutrophil count ≥1,500/mcL * platelets ≥100,000/mcL * hemoglobin \>= 9 g/dl * total bilirubin ≤1.5 × institutional upper limit of normal (ULN) * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional ULN * AST(SGOT)/ALT(SGPT) For patients with documented liver metastases, ≤ 5 × institutional ULN * creatinine ≤1.5 ×within normal institutional ULN OR * creatinine clearance ≥60 mL/min/1.73 m2 for participants with creatinine levels above institutional ULN. * International normalized ratio (INR) or Prothrombin Time (PT) \<1.5 times the upper limit of normal unless subject is receiving anticoagulant therapy, as long as PT or PTT is within therapeutic range of intended use of anticoagulants. * Activated Partial Thromboplastin Time (aPTT) \<1.5 times the upper limit of normal unless subject is receiving anticoagulant therapy, as long as PT or PTT is within therapeutic range of intended use of anticoagulants. * Laboratory tests required for eligibility must be completed within 14 days prior study entry. Baseline tumor measurements must be documented from tests within 28 days of study entry. Other non-laboratory tests must be performed within 28 days of study entry. Exclusion Criteria: * Metastatic disease impinging on the spinal cord or threatening spinal cord compression. * Surgical fixation of bone lesion to be irradiated is required and indicated to provide mechanical stability. * Known brain metastases that are untreated, symptomatic, or require therapy to control symptoms. Participants with previously diagnosed brain metastases are eligible if they have completed treatment at least 2 weeks prior to trial therapy initiation, are neurologically stable, and have recovered from the acute effects of radiotherapy or surgery. Any corticosteroid use for brain metastases must have been discontinued without the subsequent appearance of symptoms for ≥2 weeks before the initiating protocol therapy. Treatment for brain metastases may include surgery, whole brain radiotherapy, radiosurgery, or a combination as deemed appropriate by the treating physician. * Participants who are receiving any other investigational agents. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to pembrolizumab or previous toxicity attributed to pembrolizumab or other PD-1 directed therapy that led to drug discontinuation. * 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. * Clinically significant electrocardiogram (ECG) abnormality, including a marked Baseline prolonged QT/QTc (\[QT interval/corrected QT interval\], e.g., a repeated demonstration of a QTc interval \>500 ms). * Pregnant women are excluded from this study because immunotherapy has the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk of adverse events in nursing infants secondary to treatment of the mother with immunotherapy, breastfeeding should be discontinued if the mother is treated on this protocol. * Individuals with a history of a different malignancy are ineligible except for the following circumstances: if they have been disease-free for at least 2 years and are deemed by the investigator to be at low risk for recurrence of that malignancy; or if diagnosed and treated for cervical cancer in situ or basal cell or squamous cell carcinoma of the skin. * HIV-positive individuals on combination antiretroviral therapy are ineligible because of the potential for interaction between immunotherapy and these medications. * Has history of (non-infectious) pneumonitis that required steroids, evidence of interstitial lung disease or active, non infectious pneumonitis. * Active, suspected or prior documented autoimmune disease that has required systemic treatment in the last 2 years with immune modifying agents (e.g. replacement therapy such as thyroxine, insulin or physiologic corticosteroids is not an exclusion criteria). * The subject is known to be positive for HepBsAg, or HCV RNA. * Lack of availability for follow up assessments. * The investigator's belief that the subject is medically unfit to receive pembrolizumab and or unsuitable for any other reason. * Has received a live vaccine within 30 days of planned start of study therapy