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

Inclusion Criteria: * Histologically confirmed, unresectable, locally advanced, or metastatic melanoma, HCC, NSCLC, RCC, MSI-H/dMMR malignancies, urothelial carcinoma, esophageal squamous cell carcinoma, mesothelioma, SCCHN, or cervical carcinoma not amenable to standard treatment, or standard treatment is not available, or in the Investigator's opinion, the standard treatment would not be in the patient's best interest. Part A only: Evaluable only or measurable disease according to RECIST v1.1 Part B only: At least 1 measurable tumor lesion according to RECIST v1.1 * Prior treatment must include a PD-1 or programmed cell death - ligand 1 (PD-L1) inhibitor. Prior treatment with a CTLA-4 inhibitor is not required. * Eastern Cooperate Oncology Group (ECOG) performance score of 0 or 1 * Adequate bone marrow function, as determined by: * Absolute neutrophil count (ANC) ≥ 1500/ μL (should not have received growth factors within 2 weeks prior to screening) * Platelet count ≥ 75,000/ μL * Hemoglobin ≥ 8.0 g/dL (no red blood cell transfusion within 2 weeks of study treatment start is allowed) * Adequate renal function, based on estimated creatinine clearance (eCrCl) ≥ 50 mL/min, calculated by the Cockcroft-Gault equation. * Adequate hepatic function, as determined by: * Total bilirubin ≤ 1.5x upper limit of normal (ULN) or ≤ 2x ULN direct bilirubin for patients with Gilbert's Syndrome * Aspartate transaminase (AST) ≤ 3x ULN (or ≤ 5x ULN if liver metastasis or HCC). * Alanine transaminase (ALT) ≤ 3x ULN (or ≤ 5x ULN if liver metastasis or HCC). * Adequate serum albumin (albumin ≥ 2.5 g/dL) * Availability of a lesion that can be biopsied with acceptable risk. * Patients capable of bearing children must have a negative highly sensitive pregnancy test within 72 hours before the start of treatment. Patients who are postmenopausal (\> 1 year since last menstrual cycle) or permanently sterilized (e.g., bilateral tubal occlusion, hysterectomy, bilateral salpingectomy) may be considered as not of reproductive potential. * Patients of reproductive potential must agree either to abstain continuously from heterosexual intercourse or to use a highly effective birth control method from signing the informed consent form (ICF) until 30 days after the last dose of MT-8421 and/or 5 months after the last dose of nivolumab for patients capable of bearing children and until 90 days after the last dose of MT-8421 for patients capable of fathering a child. Patients must not donate sperm during the study and for 90 days after the last dose of nivolumab or MT-8421. Exclusion Criteria: * Unwilling or unable to undergo 2 sets of 3 to 6 core tumor biopsies: one set at study baseline (prior to first dose of study drug) and one set between Weeks 6 through 8. A final optional set will be collected time of disease progression. * Received approved or investigational treatment for the disease under study (except ipilimumab) where Exclusion Criterion 4 applies, requiring a washout that will be dependent upon prior ipilimumab dose and planned MT-8421 dose) within 4 weeks before the start of treatment. For small molecules \[Molecular Weight (MW) \< 0.9 kDa\], the washout is 5 half-lives, but at least 2 weeks. * Received tremelimumab within 30 days or ipilimumab 3 mg/kg within 60 days or ipilimumab 1 mg/kg within 30 days before the start of treatment. Once dose cohort of 32 µg/kg MT-8421 has been completed in dose escalation, a 30-day washout of ipilimumab is acceptable irrespective of prior dose. * Any concurrent cancer treatment, apart from local treatment of non-target lesions for palliative intent (e.g., local surgery or radiotherapy). Patient must have recovered from the effects of the local treatment and be discussed with the medical monitor. * History or current evidence of another neoplastic disease, except cervical carcinoma in situ; superficial non-invasive bladder tumors, curatively treated; Stage I to II non-melanoma skin cancer; prostate cancer managed by active surveillance; or any previous cancer curatively treated \< 2 years before the start of treatment. * Active autoimmune disease that required systemic treatment in the past. Patients who have not required systemic treatment for at least 2 years may be enrolled if permission is provided after discussion with the Medical Monitor (replacement therapy, e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency is allowed) * Evidence of active, non-infectious ≥ Grade 2 pneumonitis or current evidence of ≥ Grade 3 other underlying pulmonary disease. * Ongoing \> Grade 1 immune-related toxicity caused by prior CPI therapy (i.e., PD-1 inhibitors, PDL1 inhibitors, or CTLA-4 inhibitors). Patients with stable endocrinological AEs (e.g., hypothyroidism, adrenal insufficiency, hypopituitarism, or diabetes mellitus) must have been on a stable dose of supplemental therapy for at least 2 weeks before screening to be eligible for this study. History of repeat Grade 2 pneumonitis or myocarditis on previous CPI and/or Grade 3 irAE on previous CPI treatment. * Current evidence of new or growing central nervous system (CNS) metastases during screening. Patients with known CNS metastases will be eligible if they meet all the following criteria: * Received radiotherapy or another appropriate therapy for the CNS metastases, if clinically Indicated * Have stable CNS disease on the computed tomography (CT) or magnetic resonance imaging (MRI) scan within 4 weeks before signing the ICF compared with prior neuroimaging. * History or current evidence of significant cardiovascular disease before the start of treatment. * Current evidence of active, uncontrolled hepatitis B virus, hepatitis C virus, human immunodeficiency virus (HIV) (evidenced by detectable viral load by polymerase chain reaction) or acquired immunodeficiency syndrome (AIDS)-related illness. * Serology and virology measurements are not required to be performed at screening, but any previously reported results should be used for eligibility purposes. Investigators will test per their discretion * Patients with a history of treated hepatitis C and non-quantifiable hepatitis C virus- ribonucleic acid (RNA) may be enrolled. * Patients on treatment for hepatitis B, hepatitis C, and/or HIV will be eligible if they have undetectable viral load (patients with HIV with CD4+ T-cell \[CD4+\] counts ≥ 350 cells/µL may be enrolled). * Patients with unintentional weight loss greater than 10% of their body weight over the preceding 2 months or less prior to first dose in the first cycle.