Study of Cemiplimab - TP Induction Chemotherapy in Patients with Locally Advanced Squamous Cell Carcinoma of the Head and Neck

Inclusion Criteria:

* Patients with stage III or IV, previously untreated, non-metastatic, locally advanced HNSCC (patients may have had previous surgery, but not chemotherapy or radiotherapy).

  a) Patients with oral cancer, HPV negative oropharyngeal cancer, high risk HPV+ oropharyngeal HNSCC confirmed by PCR. Patients with unknown primary, supraglottic, nasopharyngeal, and hypopharyngeal SCC will be allowed. High risk HPV defined as one of the following: HPV 16, 18, 31, 33, 35, 39, 45, 51, 52, 56, 58, 59, 68, 73, and 82.
* A pretreatment biopsy of the primary site sufficient for immune studies is required.
* Age \>/= 18 years
* ECOG PS 0-1
* Hemoglobin \> 8.0 g/dl, absolute neutrophil count \> 1,500/mm3, platelet count \> 100,000/mm3
* Predicted life expectancy \>/= 12 weeks
* Total bilirubin \<2.5 x Upper limit of normal (ULN); AST (SGOT) \< 2.5 x ULN; ALT (SGPT) \< 2.5 x ULN; serum creatinine \</= 1.5 x ULN (Gilbert's disease allowed with elevated bilirubin)
* Patients must be accessible for repeat dosing and follow-up
* Patients - both males and females - with reproductive potential must agree to practice effective contraceptive measures throughout the study. Women of childbearing potential must provide a negative pregnancy test at baseline and on Day 1
* Patients must provide verbal and written informed consent to participate in the study.
* A biopsy of the primary tumor or lymph node must be available for testing and immune evaluation

Exclusion Criteria:

* Locally advanced EBV positive nasopharyngeal cancer, malignancies other than SCC head and neck cancer except surgically treated malignancies that are not active (e.g. surgically treated thyroid cancer, prostate cancer, breast cancer etc.) for 3 years or more and no evidence of active recurrence.
* History of pneumonitis
* History of prior immunotherapy
* History of receiving PI3K inhibitors.
* Patients at 1.5mg or more a day of dexamethasone (or equivalent).
* History of significant cardiac disease unless the disease is well-controlled
* Grade 2 peripheral neuropathy
* No excessive alcohol consumption will be allowed
* Serious comorbid illness, and involuntary weight loss of more than 20% of body weight in the 3 months preceding study entry
* History of cerebrovascular accident (CVA) within 12 months prior to registration or that is not stable
* History of any psychiatric condition that might impair the patient's ability to understand or to comply with the requirements of the study or to provide informed consent.
* Pregnant or breast-feeding females.
* GI abnormalities including inability to take oral medication, requirement for IV alimentation, active peptic ulcer, or prior surgical procedures affecting absorption
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to the study drug
* Any type of active seizure disorder
* Patients with history of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80
* Use of strong or moderate CYP3A4 or CYP1A2 inhibitors/inducers, with the exception of low- dose steroids, within 14 days prior to Day 1 dosing
* Symptomatic brain metastases that are not stable, require steroids, or that have required radiation within the last 28 days
* Active or uncontrolled infections or serious illnesses or medical conditions that could interfere with the patient's ongoing participation in the study
* History of Hepatitis c or HIV infection, autoimmune disease (except vitiligo and Hashimoto's thyroiditis), or major organ transplant
* Any irradiation or chemotherapy in the past and no major surgical procedure in the last 4 weeks
* Any other concomitant anticancer therapies
* Patients will be excluded if they received any prior chemotherapy, radiotherapy, or treatment with biologic response modifiers (except curatively treated basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix)
* History of colitis or chronic diarrheal illness
* History of, or active, co-morbid medical condition, which in the opinion of the investigator, would raise significant risk to the patient.