Background: Letetresgene autoleucel (lete-cel; GSK3377794) is an autologous T-cell therapy expressing an affinity-enhanced T-cell receptor (TCR) to improve recognition of cancer cells expressing NY-ESO-1 and/or LAGE-1a. Next generation NY-ESO-1 TCR T-cell therapy, GSK4427296, utilizes the same TCR as lete-cel, as well as an epigenetic reprogramming process (Epi-R) developed by Lyell Immunopharma to alter the phenotypic T-cell profile of the manufactured product, and is intended to increase the proportion of cells with properties of durable stemness. T cells with properties of durable stemness are able to proliferate, persist, and self-renew with anti-tumor functionality. A first-time-in-human master protocol (NCT04526509) is underway to evaluate the safety, tolerability, and recommended phase II dose (RP2D) of next generation NY-ESO-1 TCR T-cell therapies. Substudy 3 is added to this master protocol to assess GSK4427296 in patients with advanced synovial sarcoma (SS) or myxoid/round cell liposarcoma (MRCLS). Methods: This substudy includes a dose confirmation stage to assess RP2D and a dose expansion stage, aiming to dose 10 participants at the RP2D. Key inclusion criteria: age ≥18 years; measurable disease per RECIST v1.1; HLA-A*02:01, A*02:05, or A*02:06 positivity; NY-ESO-1/LAGE-1a tumor expression; advanced (metastatic/unresectable) SS with t(X;18) translocation or MRCLS with a translocation involving DDIT3 and/or FUS and/or EWSR1 genes; and anthracycline-based therapy receipt/completion/intolerance. Key exclusion criteria: prior malignancy that is not in complete remission or clinically significant systemic illness; prior receipt of gene or allogenic stem cell/solid organ transplant; and central nervous system metastases. Primary endpoints: safety (adverse events) and tolerability (dose-limiting toxicities). Secondary endpoints: investigator-assessed overall response rate, duration of response, maximum transgene expansion (C_max), T_max, and AUC_(0-t). Analyses will be descriptive. The master protocol is open for recruitment. Clinical trial information: NCT04526509.