Pulsed Dose Chemotherapy Plus Pembrolizumab in Recurrent/Metastatic HNSCC

Inclusion Criteria: 1. Recurrent/metastatic squamous cell carcinoma of the head and neck that is considered incurable by local therapies. 2. PD-L1 Combined Positive Score (CPS) \>1 3. Age \> 18 years. 4. Eastern Cooperative Oncology Group (ECOG) Performance Scale (PS) 0-2 5. Measurable disease using Response Evaluation Criteria in Solid Tumors (RECIST) 1 6. Patients must have normal organ and marrow function as defined below: 1. absolute neutrophil count ≥1,000/mcL 2. platelets ≥100,000/mcL 3. total bilirubin ≤ 1.5 X the institutional upper limit of normal (ULN) 4. AST(SGOT)/ALT(SGPT) ≤2.5 × institutional ULN (≤ 5 X the institutional ULN for patients with liver metastasis) 5. Creatinine clearance ≥40 mL/min/1.73 m2 for patients with a creatinine levels above institutional normal. 7. Female subjects of childbearing potential should have a negative urine or serum pregnancy during the screening period and also prior to receiving the first dose of study medication. If a urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. 8. Female subjects of childbearing potential should be willing to use one methods of birth control or abstain from heterosexual activity for the course of the study through 60 days after the last dose of study medication. Women of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year. 9. Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 60 days after the last dose of study therapy. 10. Ability to understand and the willingness to sign a written informed consent document. 11. If known to have prior brain metastases, must not have evidence of active (enlarging and/or symptomatic lesions) brain disease on MRI/CT evaluation done within 30 days of consent. Exclusion Criteria: 1. Patients should not have had prior systemic therapy alone administered in the recurrent/ or metastatic setting. If a patient received platinum based systemic therapy which was completed more than 6 months prior to signing consent given as part of multimodal curative intent treatment for locally advanced HNSCC (This includes both definitive concurrent chemoradiation and adjuvant chemoradiation) the patient is still eligible, 2. A patient cannot have received prior anti-PD-1 or anti-PD-L1 monoclonal antibody (mAb) therapy as systemic therapy for the treatment of recurrent/metastatic disease. Patients that received anti-PD-1 or anti-PD-L1 mAb therapy as part of multimodality curative intent treatment of locally advanced disease are still eligible as long as it has been at least 1 year since prior therapy. Patients that received anti-PD-1 or anti-PD-L1 mAb therapy as part of radiation for locoregional recurrence will be eligible as long as it has been 1 year since prior therapy. 3. Squamous cell carcinoma of the skin or of salivary gland origin. 4. Has an active autoimmune disease requiring systemic treatment within the past 3 months, or a syndrome that requires ongoing systemic steroids or immunosuppressive agents. Subjects with vitiligo, Grave's disease, or psoriasis not requiring systemic therapy or resolved childhood asthma/atopy would be an exception to this rule. Subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study. Subjects with hypothyroidism or Sjogren's syndrome will not be excluded from the study. 5. Has a history of non-infectious pneumonitis that required steroids, evidence of interstitial lung disease, or currently active non-infectious pneumonitis. 6. Prior malignancy within 2 years that in the investigator's opinion would be likely to affect the outcomes of the patients R/M HNSCC. 7. Peripheral sensory neuropathy \> grade 2 by CTCAE v5.0 8. 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. 9. Known allergy or hypersensitivity to carboplatin, other platinum agents, pembrolizumab, or paclitaxel. 10. Baseline neutrophil count of \< 1,500 cells/mm.