Study of MT-8421 as Monotherapy and in Combination With Nivolumab in Patients With Selected Advanced Solid Cancer Types

This study is conducted in two parts. The study will enroll up to 200 total participants (up to 40 in Part A and up to 160 in Part B). Part A (Dose Escalation) is designed to estimate the maximum tolerated dose (MTD) of MT-8421 as monotherapy and in combination with nivolumab. Part B (Dose Expansion) is designed to identify the dose(s) to be studied in Phase 2. The drug being tested in this study is called MT-8421. The study will evaluate safety, tolerability, efficacy, pharmacokinetics, pharmacodynamics, and immunogenicity of MT-8421 as monotherapy and in combination with nivolumab in patients with selected advanced solid cancer types. MT-8421 will be given as an intravenous (IV) infusion on Days 1, 8, 15, and 22 of a 28-day cycle. H1 and H2 blockers and anti-pyretics will be given to all patients as pre-medication prior to each dose in Cycle 1. Anti-pyretics will be required for 24 hours after the first dose in Cycle 1. Use of pre-medication will be at the discretion of the Investigator for subsequent doses. In Parts A and B, a subject may participate for the following three (3) periods: * Screening Period- up to 28 days before the first dose of MT-8421 * Treatment Period- active period where a subject will receive doses of MT-8421 over a 28-day treatment period. * Follow-up Period- up to 24 months after the second short term follow up visit. In both parts of the study, participants can receive MT-8421 until their cancer worsens, side effects prevent further study treatment, or until the participant leaves the study for other reasons decided by the participant, the study doctor, or the sponsor of the study. After the second short term follow up visit participants will have a check -up of their disease every 12 weeks for 24 months. The overall duration of the study will vary for each participant because study treatment will continue until unacceptable toxicity, withdrawal of consent, death, termination of the study by the sponsor, or fulfilment of another discontinuation criterion.