Inclusion Criteria  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. Mesothelin-expression (>=50% positive on viable tumor cells) must be determined on the tumor locally by immunohistochemistry using a validated assay, scoring and staining confirmed by the sponsor. Fresh biopsy sample must be used for eligibility assessment unless archived biopsy sample obtained within 6 months prior to leukapheresis procedures is available. Life expectancy >=12 weeks. Eastern Cooperative Oncology Group performance status of 0 or 1.  Adequate organ function as confirmed by clinical laboratory values as specified below:  Total bilirubin =<1.5 × the upper limit of the normal range (ULN) except in Participants with Gilbert's syndrome. Participants with Gilbert's syndrome may enroll with direct bilirubin =<3 × ULN of the direct bilirubin. Elevated indirect bilirubin due to posttransfusion hemolysis is allowed  Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) must be <3 × ULN.  AST and ALT may be elevated up to 5 × ULN if the elevation can be reasonably ascribed to the presence of metastatic disease in the liver.  Calculated creatinine clearance >50 mL/min (Cockcroft-Gault formula). Hemoglobin must be >=9 g/dL. Neutrophil count must be >1000/mm^3. Absolute lymphocyte count must be >500/mm^3. Platelet count must be >75,000/mm^3. Participants must have radiographically measurable disease as defined by Response Evaluation Criteria in Solid Tumors, Version 1.1 (RECIST 1.1).  Exclusion Criteria  Active systemic infections. 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. Coagulation disorders, or other major medical illnesses including respiratory or immune system disease. Participants with known cardiovascular and cardiopulmonary disease defined as unstable angina, clinically significant arrhythmia, myocardial infarction, congestive heart failure, left ventricular ejection fraction (LVEF) <45 %, baseline oxygen saturation <93% on room air. A well-controlled atrial fibrillation would not be an exclusion whereas uncontrolled atrial fibrillation would be an exclusion. Participants with any signs of lymphoma and/or leukemia. Participants who are diagnosed with or treated for another malignancy within 3 years before leukapheresis procedures. Participants with non-melanoma skin cancer or carcinoma in situ (eg, cervix, bladder, breast) would be included if they were adequately treated. Any disease requiring systemic steroid treatment. Any prior use of cell and gene therapy(ies). Treatment with any investigational products (except for cell or gene therapy) within 14 days before leukapheresis procedures or 28 days before treatment with conditioning chemotherapy/TAK-103. Systemic anticancer therapy (including immuno-oncology therapies) and treatment with radiotherapy within 14 days before leukapheresis procedures or treatment with conditioning chemotherapy/TAK-103. Treatment with major surgery within 28 days before leukapheresis procedures or treatment with conditioning chemotherapy/TAK-103 (minor surgical procedures such as catheter placement are not exclusionary criteria). Previous treatment with any mesothelin-targeted therapy. Any unresolved toxicity of Grade 3 or higher from previous anticancer therapy. Participants with risk of bleeding as judged by the investigator. Presence of central nervous system metastasis or other significant neurological conditions (Participant with central nervous system metastases that have been effectively treated where necessary and stable can be enrolled). Participants with human immunodeficiency virus (HIV) seropositive and/or human T-cell lymphotropic virus (HTLV) seropositive. Participants with a history of organ transplantation or awaiting organ transplantation. Participants with severe immediate hypersensitivity to any of the agents including cyclophosphamide, fludarabine, or streptomycin.