Neoadjuvant CADI-05 in Combination With Pembrolizumab for Surgically Resectable Locally Advanced Head and Neck Squamous Cell Carcinomas

Inclusion Criteria: * Histologically confirmed new diagnosis of resectable, non-metastatic, squamous cell carcinoma that is either: Stage III Human Papillomavirus (HPV) positive oropharyngeal primary that is tumor size (T) 4, lymph node involvement (N) 0-2, no distant metastases (M0); Stage III or IVA oropharyngeal HPV negative; or Stage III or IVA larynx/hypopharynx/oral cavity primaries (AJCC 8th edition) with programmed death ligand -1 (PD-L1) combined positive score (CPS) ≥ 1 (as determined by any clinical pathology laboratory) Patients must be planned for definitive surgical resection as determined by a multidisciplinary tumor board or equivalent multidisciplinary determination. * Patients with recurrence or metachronous primary SCC of head and neck origins with previous history of surgery/radio (chemo)-therapy are allowed if definitive surgery is planned and if pembrolizumab is planned as a neoadjuvant strategy. Patients should have recovered from the effects of radiation or other prior treatments: AE/sequelae should resolve to ≤ grade 2 (no minimum recovery period required). * Patients must have an archival biopsy from the primary tumor site or regional lymph nodal metastasis with adequate tumor tissue as judged by study PI. There should not be any oncological treatments between the pre-CADI-05 biopsy and W1 Pembrolizumab/CADI-05 treatment initiation. Note: If pretreatment material is a cytology specimen and deemed unsuitable for correlative testing, a core biopsy will be strongly recommended. * Age ≥18 years * Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2. * Patients must consent to provide either archival (if available \& sufficient) or fresh pre-treatment tissue biopsy for research, and consent for the use of their residual post-operative tissue for research. * Adequate bone marrow, liver and kidney function as demonstrated by: * Absolute neutrophil count (ANC) ≥ 1.0 x 109/L * Hgb \> 7 g/dL (use of transfusion to reach this threshold prior to study initiation is acceptable) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3.5 * upper limit of normal (ULN) * Total serum bilirubin ≤1.5 ULN * Patients with suspected Gilbert's disease may enroll provided that total bilirubin must be \< 3 mg/dL * Creatinine clearance (CrCL) \> 30 mL/min as measured via Cockcroft-Gault * Female patients must be surgically sterile or be postmenopausal or must use highly effective contraception while receiving trial treatment. * Subjects must possess the ability to understand and willingness to sign a written informed consent and HIPAA consent document. Translation services including translation of informed consent documents will be provided, as feasible, to encourage diversity of inclusion of eligible patients. Exclusion Criteria: * Patients who are considered candidates for organ preservation through upfront concurrent chemoradiation therapy will be excluded from this study. * Receiving any investigational agent currently or within 28 days of first dose of CADI-05. * Active, serious infection, medical, or psychiatric condition that would represent an inappropriate risk to the subject or would likely compromise achievement of the primary study objective, including unstable angina, serious uncontrolled cardiac arrhythmia, uncontrolled infection, or myocardial infarction ≤ 6 months prior to study entry. * Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis, Crohn's disease\]; diverticulitis with the exception of a prior episode that has resolved or diverticulosis; celiac disease; irritable bowel disease, or other serious gastrointestinal chronic conditions associated with diarrhea; systemic lupus erythematosus; Wegener's syndrome \[granulomatosis with polyangiitis\]; myasthenia gravis; rheumatoid arthritis; hypophysitis, uveitis; etc.) within the past 2 years prior to the start of treatment. NOTE: Subjects with vitiligo, Grave's disease, or psoriasis not requiring systemic treatment (within the past 2 years) are not excluded. * Other prior or concomitant malignancies with the exception of: * Non-melanoma skin cancer * In-situ malignancy or any other malignancy that does not affect the primary management of the HNSCC under consideration including delivery of neoadjuvant pembrolizumab and definitive surgery plan. * Low-risk prostate cancer after curative therapy * Other cancer for which the subject has been disease free for ≥ 2 years before the first dose of study drug and of low potential risk for recurrence. * Any concurrent chemotherapy, investigational treatment, biologic or hormonal therapy for cancer treatment except adjuvant intent hormonal therapy for definitively treated breast or prostate cancer that has not recurred in last 2 years. Concurrent use of hormonal therapy for non-cancer-related conditions (e.g. hormone replacement therapy) is acceptable. * Current or prior use of immunosuppressive medication within 14 days prior to the first dose of CADI-05. The following are exceptions to this criterion: intranasal, inhaled, topical or local steroid injections (e.g. intra-articular injection); steroids as premedication for hypersensitivity reactions; systemic corticosteroid at physiological doses not to exceed 10mg/day of prednisone or equivalent. \[NOTE: If systemic corticosteroids are part of the treatment regimen for the indication under study, the systemic corticosteroid is permitted\]. * Uncontrolled human immunodeficiency virus (HIV) infection with CD4+ T \< 200 cells/mm3. * Untreated or uncontrolled hepatitis C virus (HCV) or evidence of active hepatitis B virus (HBV). Patients with hepatitis B receiving treatment with anti- HBV therapy and having undetectable virus titers will be included. * History of primary immunodeficiency. * History of organ transplant. * Pregnant or breastfeeding. Refer to section 4.4 for further detail.