This is a multi-center, open-label Phase 2 study designed to evaluate the efficacy and safety of BA3021 as monotherapy and combination therapy in patients with recurrent or metastatic squamous cell carcinoma of the head and neck.

Inclusion Criteria:

• The eligible primary tumor locations are oropharynx, oral cavity, hypopharynx, and larynx. Patients may not have a primary tumor site of nasopharynx (any histology).
• Neoadjuvant/induction setting (Cohort N1): Patient with newly diagnosed Stage III SCCHN who are eligible for induction therapy with resectable tumors. No prior treatments, including surgery, radiation, or systemic treatment, for SCCHN are allowed.
• Recurrent or metastatic setting: Histologically or cytologically confirmed recurrent or metastatic SCCHN Stage III/IV and not amenable to local therapy with curative intent (surgery or radiation therapy with or without chemotherapy).
• First-line - Combination Cohorts (C1 and C2): Patients must have NO prior systemic therapy administered in the locally recurrent or metastatic setting. Previous treatments with PD-1/L1 inhibitor or anti-CTLA-4 treatment are not allowed.
• Second-line (Combination Cohort C3) and Second-line+ (Monotherapy Cohorts M1 and M2): Patients must have documented treatment failure of no more than one approved PD-1/L1 inhibitor either administered alone or in combination.

Patients must have measurable disease.

• Age ≥ 18 years
• Adequate renal function
• Adequate liver function
• Adequate hematological function
• Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.

Exclusion Criteria:

• Patients must not have a history of ≥ Grade 3 allergic reactions to mAb therapy as well as known or suspected allergy or intolerance to any agent given during this study.
• Patients must not have known human immunodeficiency virus (HIV) infection, active hepatitis B and/or hepatitis C.
• Patients must not be women who are pregnant or are breast feeding.