A Study to Assess the Effects of Multiple Study Drug Regimens in Subjects With Newly Diagnosed Locally Advanced Head and Neck Squamous Cell Carcinoma

* Newly diagnosed stage 3 to 4B squamous cell carcinoma of the oral cavity, oropharynx, larynx, or hypopharynx who are candidates for surgical resection and are treatment-naïve. Participants must have been determined to be candidates for surgical resection by a multidisciplinary team including a surgeon, a medical oncologist, and a radiation oncologist. * Has an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 to 1 and life expectancy of more than 3 months. * Must consent to provide the tumor tissues for analyses as described in the protocol. * Must have adequate bone marrow function (without any growth factors or transfusions within 2 weeks prior to the first dose), kidney and liver function, with all laboratory values criteria detailed in the protocol.

* Has received live vaccine within 28 days prior to the first dose of study drug. * Has a history of inflammatory bowel disease, a history of or ongoing pneumonitis or interstitial lung disease, had major surgery ≤ 28 days prior to the first dose of study drug and the surgical wound is not fully healed. * Participants with hypopharyngeal or laryngeal tumors will not be candidates for Arm 4 of the study (IT injection of ABBV-927). * Requires use of an immunosuppressive medication within 14 days prior to the first dose of the study drug; exceptions are described in the protocol. * Has a confirmed positive test results for human immunodeficiency virus, or have active hepatitis A, B or C. * Has a history of primary immunodeficiency, allogeneic bone marrow transplantation, solid organ transplantation, or previous clinical diagnosis of tuberculosis. * Has a history of any other malignancy within the past 3 years except for successfully treated non-melanoma skin cancer or localized carcinoma in situ that is considered cured or adequately treated by the investigator.