Master Protocol to Assess Safety and Dose of First Time in Human Next Generation Engineered T Cells in NY-ESO-1 and/or LAGE-1a Positive Advanced Solid Tumors

Eligibility Criteria: Inclusion criteria: * Participant must be \>=18 years of age and weighs ≥40 kg on the day of signing informed consent * Participant must be positive for HLA-A\*02:01, HLA-A\*02:05, and/or HLA-A\*02:06 alleles * Participant's tumor must have tested positive for NY-ESO-1 and/or LAGE-1a expression by a GSK designated laboratory * Performance status: Eastern Cooperative Oncology Group of 0-1 * Participant must have adequate organ function and blood cell counts 7 days prior to leukapheresis * Participant must have measurable disease according to RECIST v1.1. Additional criteria for participants with SS/ MRCLS: * Participant has advanced (metastatic or unresectable) SS or MRCLS confirmed by local histopathology with evidence of disease-specific translocation * Participant has completed at least one standard of care (SOC) treatment including anthracycline containing regimen unless intolerant to or ineligible to receive the therapy. Participants who are not candidates to receive anthracycline should have received ifosfamide unless also intolerant to or ineligible to receive ifosfamide. Participants who received neoadjuvant/adjuvant anthracycline or ifosfamide based therapy and progressed will be eligible Additional criteria for participants with non-small cell lung cancer (NSCLC): * Participant has Stage IV NSCLC as confirmed by histology or cytology * Prior therapies for participants lacking actionable genetic aberrations (i.e., wild type), per National C…