Inclusion Criteria:

          -  Parts 1 and 3 (escalation cohorts): 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.

          -  Parts 2 and 4 (expansion cohorts): Patients with non-small cell lung cancer, melanoma,
             head and neck squamous cell carcinoma, gastric or gastro-esophageal junction
             adenocarcinoma, renal cell carcinoma, or urothelial (transitional) cell carcinoma,
             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 treatment naive NSCLC cohort: Locally advanced or metastatic, non-resectable
             NSCLC, who have not received prior systemic treatment, including CPI, for advanced or
             metastatic disease. PD-L1 IHC Tumor Proportion Score (TPS) ≥ 1% and < 50%. In Part 4,
             all patients with non-squamous NSCLC must have documentation of absence of tumor
             activating EGFR mutations and absence of ALK gene rearrangements.

          -  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) infection
             for Part 1. 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) for Part 1. 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.