Key Inclusion Criteria:

          1. Has a histologically- or cytologically-diagnosed solid tumor which is advanced or
             metastatic and which has progressed on or following at least one systemic therapy
             regimen administered for advanced or metastatic disease or for which no approved
             therapy exists. Subject's prior treatment should include all approved regimens that
             have demonstrated a survival advantage for the subject's disease, stage, and line of
             therapy.

          2. Is aged ≥18 years at the time of signing the ICF

          3. Has provided written informed consent

          4. Has an ECOG Performance Status of 0 or 1

          5. Has measurable disease per RECIST 1.1

          6. Has an adequate tumor sample.

          7. Has adequate liver, renal, hematologic, pulmonary, cardiac, and coagulation function.

          8. Has a negative serum pregnancy test (for women of child-bearing potential) at
             Screening and a negative urine pregnancy test on Day 1 prior to the first dose of MPT
             0118

          9. Ability to swallow and retain and absorb oral medications in tablet or crushed form
             orally or via feeding tube (e.g., nasogastric feeding tube or percutaneous endoscopic
             gastrostomy feeding tube)

        Key Exclusion Criteria:

          1. Has received cytotoxic chemotherapy, biologic agent, investigational agent, checkpoint
             inhibitors, or radiation therapy ≤3 weeks prior to the first dose of MPT-0118

          2. Has received small-molecule kinase inhibitors or hormonal agents ≤14 days prior to the
             first dose of MPT-0118

          3. Has been previously treated with a MALT1 inhibitor

          4. Has clinically significant AEs that have not returned to baseline or ≤Grade 1 based on
             National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE)
             v5.0

          5. Has received systemic immunosuppressive agents within 14 days of the first dose of
             MPT-0118

          6. Has undergone major surgery ≤6 weeks or minor surgery ≤14 days prior to the first dose
             of MPT-0118

          7. Has clinically significant intercurrent disease

          8. Part B and Part C: Has previously been treated with PD-1, PD-L1, or CTLA-4 inhibitors
             and required dose-interruption, permanent discontinuation, or systemic
             immunosuppression due to immune-related AEs

          9. Has primary central nervous system (CNS) tumors or brain or leptomeningeal metastasis.

         10. Has human immunodeficiency virus (HIV) infection

         11. Has active hepatitis B or C infection

         12. Women who are pregnant or breastfeeding

         13. Has an unwillingness or inability to comply with procedures required in this protocol

         14. Is currently receiving any other anticancer or investigational agent