Study of MT-6402 in Subjects With Advanced Solid Cancer That Expresses PD-L1

This study will be conducted in two sequential parts: * Part 1 (Dose Escalation): The purpose of Part 1 is to evaluate the safety and tolerability of MT-6402 in subjects with advanced cancer (solid tumors) and to estimate the maximum tolerated dose (MTD) * Part 2 (Dose Expansion): The purpose of Part 2 is to confirm the recommended Phase 2 dose (RP2D) and to evaluate the efficacy of MT-6402 in subjects with advanced cancer. Part 2 will include subjects with PD-L1 positive non-small cell lung cancer (NSCLC) who received prior PD-1/PD-L1 treatment, subjects with PD-L1 positive squamous cell cancer of the head and neck (SCCHN) who are refractory to or ineligible for platinum-based therapy and received prior PD-1/PD-L1 treatment and subjects with any other relapsed or refractory PD-L1 positive solid tumor who received PD-1/PD-L1 treatment. Up to 138 eligible subjects will be identified and treated through competitive enrollment at multiple study centers In Parts 1 and 2, a subject may participate for the following four (4) periods: * Screening Period - up to 28 days before first dose of MT-6402 * Treatment Period - active period where a subject will receive doses of MT-6402 over a 28-day treatment period * Short-term Follow-up Period - up to 90 days after last dose of MT-6402 * Long-term follow-up Period - up to 24 months after last dose of MT-6402 MT-6402 will be given as an intravenous (IV) infusion over 30 minutes on the same day every week (i.e., days 1, 8, 15 and 22) of each cycle. A cycle is defined as 28 days. A subject can continue receiving MT-6402 as long as it is well-tolerated or until the subject decides they no longer want to participate in the study.