The purpose of this study is to test the safety of palliative "QUAD SHOT" radiotherapy combined with pembrolizumab and evaluate the effects of the combination treatment patients with recurrent cancer of head and neck.

During this study, patients will receive infusions of pembrolizumab with radiotherapy (palliative QUADSHOT regimen). The patient will receive treatment of pembrolizumab once every 3 weeks and palliative "QUAD SHOT" radiotherapy every 4 weeks. These 28 day period of time is called a cycle. The cycle will be repeated 3 times. Each cycle is numbered in order. The patient will be treated for up to 3 cycles followed by pembrolizumab single drug until unacceptable toxicity or tumor progression.

The patient will also complete a survey.

Total duration of the study is up to two years.

Inclusion Criteria:

1. Age 18 years and older
2. Written informed consent and any locally-required authorization obtained from the patients prior to performing any protocol-related procedures, including screening evaluations
3. Pathologically (histologically or cytologically) proven diagnosis of squamous cell carcinoma of the head and neck (nasopharynx, oral cavity, oropharynx, hypopharynx, larynx, or unknown primary).
4. Locally recurrent or metastatic HNSCC not deemed amenable to curative-intent salvage therapy, in whom at least six months have passed since their prior RT, if received.
5. Must have evaluable lesion per RECIST v1.1
6. Patients agree to provide their smoking history prior to registration
7. ECOG performance status of 0-2
8. Adequate bone marrow: absolute neutrophil count ≥ 1,500/μl, platelets ≥ 100,000/μl, hemoglobin ≥ 9 g/dL
9. Adequate hepatic function: total bilirubin ≤ 1.5 X upper normal limit (UNL) (except subjects with Gilbert syndrome, who can have total bilirubin < 3 mg/dl), aspartate aminotransferase (AST) ≤ 2.5 X UNL, alanine aminotransferase (ALT) ≤ 2.5 X UNL
10. Adequate renal function: calculated serum creatinine clearance >40 mL/min by the Cockcroft-Gault formula or by 24-hour urine collection or Serum creatinine less than or equal to 1.5 x upper limit of normal (ULN)
11. Female patients of reproductive potential and their male partners must agree to practice total abstinence or use a highly effective method of contraception (failure rate < 1% per year) prior to study entry, during treatment and for 90 days following the last dose of study treatment.
12. Male patient agrees to use an adequate method of contraception

Exclusion Criteria:

1. Histologically confirmed other types (Non-SCC) of salivary gland cancer

2. History of another primary malignancy EXCEPT For:

   1. malignancy treated with curative intent and with no known active disease ≥5 years before the first dose of study drug and of low potential risk for recurrence;
   2. adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease; adequately treated carcinoma in situ without evidence of disease (eg, carcinoma in situ of the breast, oral cavity and cervix are all permissible);
   3. low to favorable intermediate risk prostate cancer based on NCCN criteria on active surveillance, .

3. Prior radiotherapy to the region of the study cancer within less than 6 months

4. Patients who have received prior radiation therapy and who, in the opinion of the treating radiation oncologist, cannot be reirradiated safely without excess risk of severe toxicity given prior radiation dose to critical structures.

5. Patients with known contraindications to radiotherapy, including inherited syndromes associated with hypersensitivity to ionizing radiation (e.g., Ataxia-Telangiectasia, Nijmegen Breakage Syndrome)

6. Patients with inadequate renal function or other contraindications to IV contrast

7. Any previous treatment with PD-1 or PD-L1 inhibitors, including pembrolizumab

8. Current or prior use of immunosuppressive medication within 28 days before the first dose of pembrolizumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed 10 mg/day of prednisone, or an equivalent corticosteroid

9. Any unresolved toxicity (>CTCAE grade 2) from previous anti-cancer therapy

10. Any prior Grade ≥3 immune-related adverse event (irAE) while receiving any previous immunotherapy agent, or any unresolved irAE >Grade 1

11. Active or prior documented autoimmune disease within the past 2 years (subjects with vitiligo, Grave's disease, or psoriasis not requiring systemic treatment within the past 2 years are not excluded)

12. Patients with evidence of interstitial lung disease or active, non-infectious pneumonitis

13. History of primary immunodeficiency

14. History of allogeneic organ transplant

15. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, active peptic ulcer disease or gastritis, active bleeding diatheses including any subject known to have evidence of acute or chronic hepatitis B, hepatitis C or human immunodeficiency virus (HIV), or psychiatric illness/social situations that would limit compliance with study requirements or compromise the ability of the subject to give written informed consent

16. Severe, active co-morbidity, defined as follows:

    1. Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months
    2. Transmural myocardial infarction within the last 6 months
    3. Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration
    4. Chronic Obstructive Pulmonary Disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy within 30 days of registration
    5. Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects
    6. Known history of active infection including tuberculosis

17. Female patients who are pregnant or breastfeeding or male or female patients of reproductive potential who are not willing to employ effective birth control from screening to 90 days after the last dose of pembrolizumab.