Inclusion Criteria:

        Part A

          1. Subject must be at least 18 years old and must have histologically confirmed,
             unresectable, locally advanced, or metastatic PD-L1-expressing solid cancer 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 subject's best
             interest. Any level of PD-L1 expression assessed by using any Food and Drug
             Administration (FDA) approved PD-L1 immunohistochemistry (IHC) assay is accepted. The
             assessment should have been performed on the most recent available tissue from a site
             of metastatic disease (if possible).

          2. Subject must have evaluable or measurable disease.

        Part B

          1. Subject must be at least 18 years old and must have histologically confirmed,
             unresectable, locally advanced or metastatic PD-L1-expressing solid cancer (defined
             below) 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 subject's
             best interest. PD-L1 expression must be assessed at screening by the study's central
             laboratory, using VENTANA SP263 PD-L1 assay on a tissue from a site of metastatic
             disease (if possible). For this purpose, recent archived tissue suitable for PD-L1
             expression assessment by IHC (obtained after the last treatment and within 6 months)
             or fresh biopsy material can be used. The PD-L1 assessment must show at least 5% vCPS
             (visually estimated Combined Positive Score) for eligibility.

               -  Arm 1: Histologically confirmed recurrent or metastatic NSCLC 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 subject's best
                  interest. NOTE: subjects with driver mutations are only eligible if they have
                  received all appropriate targeted therapies.

               -  Arm 2: Histologically confirmed recurrent or metastatic SCCHN (oral cavity,
                  oropharynx, hypopharynx, or larynx) 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 subject's best interest. Subjects who
                  refuse radical resection are eligible. NOTE: squamous cell carcinoma of any other
                  primary anatomic location in the head and neck, subjects with SCCHN of unknown
                  primary, and subjects with skin squamous cell carcinoma (SCC) of the head and
                  neck are not eligible for this arm. The tumor must be platinum resistant or the
                  subject ineligible for platinum therapy due to hypersensitivity or concerns with
                  ototoxicity.

               -  Arm 3: Subjects with any other relapsed or refractory PD-L1 positive solid tumor
                  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 subject's
                  best interest, who received PD-1/PD-L1 treatment. Subjects with PD-L1 positive
                  solid tumor types, for which PD-1/PD-L1 treatment is not approved, could be
                  enrolled at the Investigator's discretion and after discussion with the Medical
                  Monitor.

          2. Subject must have at least 1 measurable tumor lesion according to RECIST 1.1.

             Parts A and B

          3. Subject must have Eastern Cooperative Oncology Group (ECOG) performance score of 0 or
             1.

          4. Prior treatment must include a CPI (i.e., PD-1 inhibitors, PD-L1 inhibitors with or
             without CTLA-4 inhibitors) if there is an approved CPI for the specific cancer type.
             Subjects may also have received CPIs in an investigational setting. Subjects who have
             not received a CPI and where there is no approved CPI for the specific cancer type
             could be enrolled at the Investigator's discretion and after discussion with the
             Medical Monitor.

          5. Subject must have adequate bone marrow function (NOTE: administration of blood
             products and growth factors is not allowed within 2 weeks prior to screening
             laboratory tests):

               -  absolute neutrophil count (ANC) ≥ 1,500/μL

               -  platelet count ≥ 100,000/μL

               -  hemoglobin ≥ 8.0 g/dL

          6. Subject must have adequate renal function, based on estimated creatinine clearance
             (eCrCl) ≥ 50 mL/min, calculated by the Cockcroft-Gault equation.

             NOTE: At the Investigator's discretion, the eCrCl result < 50 mL/min may be verified
             by measured creatinine clearance (mCrCl) based on the 24-hour urine collection.
             Subjects with mCrCl ≥ 50 mL/min will be eligible irrespective of the eCrCl result
             calculated by the Cockcroft-Gault equation.

          7. Subject must have adequate hepatic function, as determined by:

               -  total bilirubin (or direct bilirubin for subjects with Gilbert's disease) < 1.5 ×
                  upper limit of normal (ULN)

               -  aspartate aminotransferase (AST) ≤ 3 × ULN (or ≤ 5 × ULN if liver metastasis)

               -  alanine aminotransferase (ALT) ≤ 3 × ULN (or ≤ 5 × ULN if liver metastasis)

          8. Subject must have adequate serum albumin (albumin ≥ 2.5 g/dL)

          9. Women of reproductive potential must have a negative highly sensitive pregnancy test
             within 72 hours before the start of treatment. Women 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.

         10. Subjects 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 until 30 days after the last dose of MT-6402 for females
             and until 90 days after the last dose of MT-6402 for males.

        Exclusion Criteria:

        Part A

        1. Subjects without available tissue from a site of metastatic disease or easily biopsiable
        lesion (biopsy sites of non significant risk, in the opinion of the Investigator) or
        unwilling to consent to biopsy.

        Part B

          1. Subjects without easily biopsiable lesions (biopsy sites of non significant risk, in
             the opinion of the Investigator) or unwilling to consent to biopsy.

             Parts A and B

          2. History or current evidence of another neoplastic disease, except cervical carcinoma
             in situ, superficial noninvasive bladder tumors, curatively treated Stage I to II non
             melanoma skin cancer or any previous cancer curatively treated > 2 years before the
             start of treatment.

          3. Active autoimmune disease currently under treatment or required systemic treatment
             within 2 years (replacement therapy, e.g., thyroxine, insulin, or physiologic
             corticosteroid replacement therapy for adrenal or pituitary insufficiency is allowed).
             Subjects who have not required systemic treatment of an auto-immune disease for at
             least 2 years may be enrolled if permission is provided after discussion with the
             Medical Monitor.

          4. Ongoing > Grade 1 immune related toxicity caused by prior CPI therapy (i.e., PD-1
             inhibitors, PD-L1 inhibitors, or CTLA-4 inhibitors). Subjects 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.

          5. Evidence of active noninfectious ≥ Grade 2 pneumonitis or current evidence of ≥ Grade
             3 other underlying pulmonary disease.

          6. Received any of the following PD-L1 inhibitors within the following time periods prior
             to the first dose of MT-6402: atezolizumab - 12 months; durvalumab - 7 months;
             avelumab - 2 months.

          7. Any concurrent cancer treatment, apart from local treatment of non-target lesions for
             palliative intent (e.g., local surgery or radiotherapy).

          8. Prior radiation therapy within 4 weeks before the start of study treatment. NOTE: A
             lesion in a previously irradiated area can only be considered target lesion if there
             has been radiographical disease progression since the end of radiation therapy.

          9. Received approved or investigational treatment for the disease under study (except PD
             L1 inhibitors where exclusion criterion 6 applies) within 4 weeks before the start of
             treatment. For small molecules (MW < 0.9 kDa), the washout is 5 half-lives, but at
             least 2 weeks.

         10. Subjects who have had allogeneic tissue or solid organ transplantation.

         11. Current evidence of new or growing central nervous system (CNS) metastases during
             screening. Subjects with known asymptomatic CNS metastases will be eligible if they
             meet all the following criteria:

               1. Had radiotherapy or another appropriate therapy for the CNS metastases.

               2. Have stable CNS disease on the computed tomography (CT) or magnetic resonance
                  imaging (MRI) scan within 4 weeks before screening compared with prior neuro
                  imaging.

         12. Major surgical procedure (as defined by the Investigator) within 28 days prior to the
             start of study treatment.

         13. History or current evidence of significant cardiovascular disease before the start of
             treatment, including but not limited to the following conditions:

               1. Angina pectoris requiring anti-anginal medication, (chest pain: Common
                  Terminology Criteria for Adverse Events [CTCAE] Grade ≥ 2)

               2. Clinically significant valvular disease.

               3. Myocardial infarction within 12 months prior to the start of treatment.

               4. Arterial thrombosis or pulmonary embolism within 3 months before the start of
                  treatment.

               5. History of Grade ≥ 2 symptomatic congestive heart failure (CHF) or New York Heart
                  Association (NYHA) criteria Class ≥ II.

               6. Left ventricular ejection fraction (LVEF) < 55%, assessed preferably by
                  echocardiogram (ECHO) or multiple-gated acquisition (MUGA) scan if ECHO is not
                  available, within 28 days before starting study treatment.

               7. High-risk uncontrolled arrhythmias (i.e., atrial tachycardia with a heart rate >
                  100/min at rest and upon repeated testing, significant ventricular arrhythmia
                  (CTCAE Grade ≥ 2 [ventricular tachycardia], or higher-grade atrioventricular
                  [AV]-block [second degree AV-block Type 2 [Mobitz 2] or third-degree AV-block])
                  or left ventricular bundle branch block. Subjects receiving digoxin, calcium
                  channel blockers, or beta adrenergic blockers are eligible at the Investigator's
                  discretion after consultation with the Medical Monitor if the dose has been
                  stable for ≥ 2 weeks before the start of treatment with MT-6402.

               8. Any of the following within 3 months before the start of treatment: pericarditis
                  (any CTCAE Grade), pericardial effusion (CTCAE Grade ≥ 2), non-malignant pleural
                  effusion (CTCAE Grade ≥ 2) or malignant pleural effusion (CTCAE Grade ≥ 3)
                  (subjects with pleural effusion that is manageable and stable > 3 months prior to
                  study are eligible).

               9. QT interval correction for heart rate using Fridericia's formula (QTcF) ≥ 470 ms
                  (average from 3 QTcF values on the triplicate 12-lead electrocardiogram [ECG]) at
                  screening. In subjects with right bundle branch blocks, additional corrections
                  will be performed to calculate the QT equivalent JT, and depending on the result
                  the subject may be eligible with the agreement of the Medical Monitor.

         14. Current evidence of uncontrolled human immunodeficiency virus (HIV), hepatitis B virus
             (HBV), or hepatitis C virus (HCV) at screening. Serology testing is not required if
             seronegativity is documented in the medical history, and if there are no clinical
             signs suggestive of HIV or hepatitis infections, or suspected exposure. The following
             exceptions apply for subjects with positive viral serology:

               1. Subjects with HIV and an undetectable viral load and CD4 + T-cell (CD4+) counts ≥
                  350 cells/mL may be enrolled, but must be taking appropriate opportunistic
                  infection prophylaxis, if clinically relevant.

               2. Subjects with positive HBV serology are eligible if they have an undetectable
                  viral load and the subject will receive antiviral prophylaxis for potential HBV
                  reactivation per institutional guidelines.

               3. Subjects with positive HCV serology are eligible if quantitative polymerase chain
                  reaction (PCR) for plasma HCV RNA is below the lower limit of detection.
                  Concurrent antiviral HCV treatment per institutional guidelines is allowed.

         15. Current treatment requiring systemic steroids at doses > 10 mg/day prednisone
             equivalent.

         16. Subjects with a history of hypersensitivity or serious toxic reactions to kanamycin or
             other aminoglycosides.

         17. Subjects with unintentional weight loss > 10% of their body weight over the preceding
             2 months or less before screening.

         18. Female subjects who are pregnant or breastfeeding.

         19. History or evidence of any other clinically significant disorder, condition or disease
             (with the exception of those outlined above) that, in the opinion of the Investigator
             or Medical Monitor, if consulted, would pose a risk to subject safety or interfere
             with the study evaluation, procedures or completion.