A Study of TAK-103 in Adult With Solid Tumors

In this study, people with mesothelin-expressing advanced or metastatic solid tumors will receive TAK-103 with their white blood cells. The main aims of this study are to check if the participants get any side effects from treatment with TAK-103 and to check how much TAK-103 participants can receive without getting side effects from it. Researchers can then work out the best dose of TAK-103 to give to participants in future studies. At the first visit, the study doctor will check who can take part. For those who can take part, the study doctors will collect white blood cells from each participant. These cells are sent to the laboratory where TAK-103 is added to each participant's cells. This can take up to 4 or 5 weeks. Participants may receive specific treatments while participants are waiting for TAK-103. Then, participants will receive TAK-103 with their cells slowly through a vein (infusion). Participants will receive lower to higher doses of TAK-103. Each participant will just receive 1 dose. The study doctors will check for side effects after each different dose of TAK-103. In this way, researchers can work out the best dose of TAK-103 to give to participants in future studies. Participants will stay in hospital for 28 days or longer for their treatment. Then, participants will visit the clinic for regular check-ups for up to 3 years.

Inclusion Criteria 1. Histologically or cytologically confirmed advanced or metastatic solid tumors who have no option with or are intolerant of standard therapies with a proven clinical benefit. 2. Mesothelin-expression (\>=50% positive on viable tumor cells) must be determined on the tumor by immunohistochemistry using a validated assay, scoring and staining confirmed by the sponsor prior to leukapheresis procedures. 3. Life expectancy \>=12 weeks. 4. Eastern Cooperative Oncology Group performance status of 0 or 1. 5. Adequate organ function as confirmed by clinical laboratory values as specified below: 1. Total bilirubin =\1000/mm\^3. 6. Absolute lymphocyte count must be \>500/mm\^3. 7. Platelet count must be \>75,000/mm\^3. 6. Participants must have radiographically measurable disease as defined by Response Evaluation Criteria in Solid Tumors, Version 1.1 (RECIST 1.1). Exclusion Criteria 1. Active systemic infections. 2. Known hepatitis B surface antigen (HBsAg) positive, or known or suspected active hepatitis C virus (HCV) infection. Participants who have positive hepatitis B core antibody (HBcAb) or hepatitis B surface antibody (HBsAb) can be enrolled but must have an undetectable hepatitis B virus (HBV) viral load. Participants who have positive hepatitis C virus antibody (HCVAb) must have an undetectable HCV viral load. 3. Coagulation disorders, or other major medical illnesses including respiratory or immune system disease. 4. Participants with high tumor burden at the disease assessment at screening. The tumor burden is determined by the threshold set for each type of cancer. 5. Participants with current or history of interstitial lung disease. 6. Participants with current or history of significant immune-related adverse events (irAEs) related to treatment with immune checkpoint inhibitors. Patients with current or history of the following adverse events (AEs) can be enrolled after careful discussion between the investigator and sponsor: hyperglycemia/diabetes mellitus, thyroid disorder, hypopituitarism, hypoadrenocorticism, asymptomatic elevation in amylase/lipase, and Grade1 or 2 skin toxicity. 7. Participants with known cardiovascular and cardiopulmonary disease defined as unstable angina, clinically significant arrhythmia, myocardial infarction, congestive heart failure, left ventricular ejection fraction (LVEF) \