Study of MT-302 in Adults With Advanced or Metastatic Epithelial Tumors

Inclusion Criteria: 1. Adults age ≥ 18 inclusive at the time the Informed Consent Form (ICF) is signed. 2. Histologically proven, metastatic or advanced epithelial cancer including the following cancer types: 1. Urothelial 2. Cervical 3. Ovarian epithelial 4. Triple-negative breast 5. HR+/HER2- breast 6. Pancreatic ductal adenocarcinoma 7. Gastric adenocarcinoma 8. Esophageal carcinoma 9. Non-small cell lung 10. Colorectal 3. Progressive disease at baseline, refractory or relapsed to standard of care or who have declined standard therapy. 4. Measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) criteria v 1.1. 5. Eastern Cooperative Oncology Group (ECOG) performance status grade of 0 or 1. 6. Life expectancy of \> 12 weeks. 7. Echocardiogram (ECHO) or multiple gated acquisition scan showing an ejection fraction greater than or equal to 50%. 8. Electrocardiogram (ECG) showing no clinically significant abnormality at Screening or showing an average QTc interval \< 450 msec in males and \< 470 msec in females (\< 480 msec for participants with bundle branch block). Either Fridericia's or Bazett's formula may be used to correct the QT interval. 9. Oxygen saturation of greater than or equal to 90% on room air measured by pulse oximetry. 10. Adequate organ function as defined by laboratory values at Screening. 11. Willing and able to provide written informed consent. 12. Willing to perform and comply with all study procedures including undergoing study-related biopsies and attending clinic visits as scheduled. 13. Men must abstain from sperm donation during study treatment or for 4 months following last dose of study treatment. 14. Men and WOCBP must be willing to practice a highly effective method of contraception. Exclusion Criteria: 1. Known active CNS metastasis and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, (ie, without evidence of progression for at least 4 weeks by repeat imaging), clinically stable, and without requirement of steroid treatment for at least 14 days prior to the first dose of study intervention. 2. Pregnant or nursing women. 3. Must be \> 28 days beyond major surgery, including hepatectomy or joint replacement. 4. Prior allogeneic bone marrow transplantation or solid organ transplant. 5. Spinal cord compression not definitively treated with surgery and/or radiation. 6. Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures. 7. Any acute illness including fever (\> 100.4° F or \> 38° C) within 7 days prior to Day 1 8. Active systemic bacterial, fungal, or viral infection within 7 days prior to Day 1. Participant cannot have tested positive for COVID-19 within 7 days prior to Day 1. 9. Active infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV), hepatitis C virus (HCV). 10. Other primary malignancies, except: 1. Adequately treated basal cell or squamous cell carcinoma 2. In situ carcinoma of the cervix or bladder, treated curatively and without evidence of recurrence for at least 2 years prior to the study, or 3. A primary malignancy which has been completely resected and in complete remission for at least 2 years 11. History of (noninfectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. 12. Prior grade \> 3 immune-related AEs such as pneumonitis, colitis, hepatitis, nephritis; prior dermatitis and endocrinopathies are allowed provided corticosteroids are no longer required and endocrine-replacement therapy is stable and discontinued from prior therapy. 13. Active autoimmune disease not related to prior therapy for primary malignancy that has required systemic therapy in the last 1 year. 14. History of symptomatic congestive heart failure (New York Heart Association classes II-IV) or serious active arrhythmias or other clinically significant cardiac disease within 12 months of enrollment. 15. Toxicity from previous anti-cancer therapy defined as toxicities (other than alopecia, or laboratory values listed above) not yet resolved to NCI CTCAE v5.0 Grade ≤ 1 or baseline. Participants with chronic Grade 2 toxicities (eg, peripheral neuropathy, laboratory values) may be eligible per the discretion of the Investigator and Medical Monitor. 16. Has received: 1. Radiotherapy within 2 weeks of first administration of MT-302 2. Cytotoxic chemotherapy for treatment of the primary malignancy within 28 days or 5 half-lives, whichever is shorter, of administration of MT-302 3. Immune therapy for primary malignancy (eg, monoclonal antibody therapy, checkpoint inhibitors) within 28 days or 5 half-lives, whichever is shorter of first administration of MT-302 4. Targeted therapies for primary malignancy within 28 days or 5 half-lives, whichever is shorter, of first administration of MT-302 5. Anti-cancer vaccine within 12 weeks of first administration of MT-302 6. COVID-19 mRNA vaccine within 6 weeks of first administration of MT-302 17. Has received a live vaccine ≤ 6 weeks prior to first administration of MT-302 18. Has received packed red blood cells or platelet transfusion within 2 weeks prior to first administration of MT-302 19. History of an allergic reaction to any of the excipients 20. Enrollment in another interventional clinical trial within 28 days or 5 half-lives of the drug, whichever is shorter, of first administration of MT-302 21. Any other condition that, in the opinion of the Investigator, would make the participant unsuitable for the study or unable to comply with the study requirements.