Study of INBRX-105 and INBRX-105 With Pembrolizumab in Patients With Solid Tumors Including Head and Neck Cancer

Inclusion Criteria: * Parts 1 and 3 (escalation cohorts; completed): Patients with locally advanced or metastatic non-resectable solid tumors, whose disease has progressed despite standard therapy and for whom no further standard therapy exists. * Part 2 (expansion cohorts): Patients with non-small cell lung cancer, cutaneous melanoma, head and neck squamous cell carcinoma or solid tumors amenable to paired biopsies, with locally advanced or metastatic, non-resectable disease, which has progressed despite standard therapy or for whom no standard or clinically acceptable therapy exists. * Part 4 relapsed or refractory to CPI cohorts: NSCLC, cutaneous melanoma, HNSCC, MSI/TMB-high or MMRd solid tumors * Part 4 CPI naive cohorts: locally advanced or metastatic, non-resectable NSCLC or HNSCC * Refractory or relapsed to anti-PD-1 or anti-PD-L1, and anti-CTLA4 if applicable (NOTE: For all tumor types with checkpoint inhibitor approvals) with exception of the treatment naive NSCLC cohort. * PD-L1 positivity by immunohistochemistry (IHC): Parts 1 and 3 (escalation cohorts) PD-L1 positivity is not required. Parts 2 and 4 (expansion cohorts): Combined Positive Score (CPS) or Tumor Proportion Score (TPS) above certain thresholds as defined per protocol. * Adequate hematologic, coagulation, hepatic and renal function as defined per protocol. * Eastern Cooperative Oncology Group performance status (ECOG PS) of 0 or 1. Exclusion Criteria: * Prior exposure to 4-1BB agonists. * Receipt of any investigational product or any approved anticancer drug(s) or biological product(s) within 4 weeks prior to the first dose of study drug. Exceptions: Hormone replacement therapy, testosterone, or oral contraceptives. NOTE: Previous exposure to anti-PD-L1 checkpoint inhibitor requires a minimum washout period of 24 weeks prior to the first dose of study drug. * Hematologic malignancies (e.g., ALL, AML, MDS, CLL, CML, NHL, Hodgkin lymphoma and multiple myeloma). * Prior or concurrent malignancies. Exception: Subjects with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessments of INBRX-105. * Known or active primary central nervous system (CNS) tumors, leptomeningeal disease and CNS metastases. Exception: Subjects with previously treated, asymptomatic, and clinically stable CNS metastases may be allowed study entry if certain criteria apply. * Grade ≥ 3 immune-related adverse events (irAEs) or irAE that lead to discontinuation of prior immunotherapy. Some exceptions as defined per protocol apply. * Active autoimmune disease or documented history of autoimmune disease that required systemic steroids or other immunosuppressive medications. Certain exceptions as defined in protocol apply. * Treatment with systemic immunosuppressive medications within 4 weeks prior to the first dose of study drug. Certain exceptions as defined in protocol apply. * History of hepatitis B, hepatitis C, or human immunodeficiency virus (HIV). Exceptions as defined in protocol for expansion cohorts will apply. * History of hepatitis or cirrhosis (e.g., non-alcohol steatohepatitis, alcohol or drug-related, autoimmune, hepatitis B, or hepatitis C). Exceptions as defined in protocol for expansion cohorts will apply. * Active interstitial lung disease (ILD) or pneumonitis or a history of ILD or pneumonitis requiring treatment with steroids or other immunosuppressive medications. * Clinically significant cardiac condition, including myocardial infarction, uncontrolled angina, cerebrovascular accident, or other acute uncontrolled heart disease \< 3 months; left ventricular ejection fraction (LVEF) \< 50%; New York Heart Association (NYHA) Class III or IV congestive heart failure; or uncontrolled hypertension. * Active, hemodynamically significant pulmonary embolism within 3 months prior to enrollment on this trial. * Major surgery within 4 weeks prior to enrollment on this trial. * Anti-infectious drug treatments (i.e., antibiotics) within 4 weeks prior to the first dose of study drug. * Prior organ allograft transplantations or allogeneic peripheral blood stem cell (PBSC) or bone marrow (BM) transplantation.