ADP-A2M4CD8 as Monotherapy or in Combination With Either Nivolumab or Pembrolizumab in HLA-A2+ Subjects With MAGE-A4 Positive Tumors (SURPASS)

* Key Inclusion criteria * Age ≥18 and ≤ 75 years * Subject is positive for at least 1 HLA-A\*02 inclusion allele * Histologically or cytogenetically confirmed diagnosis of urothelial cancer, esophageal, esophagogastric junction (EGJ) cancer, gastric cancer, non-small cell lung carcinoma (NSCLC), head and neck or ovarian cancer, endometrial cancer, melanoma * Measurable disease according to RECIST v1.1 prior to leukapheresis and lymphodepletion. * Tumor shows MAGE-A4 expression as confirmed by central laboratory * ECOG Performance Status of 0 or 1. * Left ventricular ejection fraction (LVEF) ≥50% or the institutional lower limit of normal range, whichever is lower Note: other protocol defined Inclusion/Exclusion criteria may apply * Subjects must have ≥ 90% room air oxygen saturation at rest at Screening (within 7 days of leukapheresis) and at Baseline. Key exclusion criteria * Positive for any HLA-A\*02 allele other than: one of the inclusion alleles * History of allergic reactions attributed to compounds of similar chemical or biologic composition to fludarabine, cyclophosphamide or other agents used in the study * Active autoimmune or immune mediated disease * Leptomeningeal disease, carcinomatous meningitis or symptomatic CNS metastases * Other prior malignancy that is not considered by the Investigator to be in complete remission. Clinically significant cardiovascular disease * Uncontrolled intercurrent illness * Active infection with human immunodeficiency virus, hepatitis B virus, hepatitis C virus, or human T cell leukemia virus * Pregnant or breastfeeding Note: other protocol defined Inclusion/Exclusion criteria may apply.