Background: Myxoid/round cell liposarcomas (MRCLS) account for 6-10% of soft tissue sarcomas. Although a chemosensitive tumor, metastatic MRCLS has a poor prognosis and is inevitably fatal. More effective, durable and less toxic therapies are needed. NY-ESO-1 is a cancer/testis antigen that is expressed in 80-90% of MRCLS tumors. This study will evaluate the safety and efficacy of genetically engineered affinity enhanced autologous NY-ESO-1^c259T cells recognizing an NY-ESO-1 derived peptide complexed with HLA-A*02 in MRCLS. Methods: This open label phase I/II non-randomized pilot study will evaluate efficacy (overall response rate by RECIST v1.1, time to response, duration of response, progression free survival, overall survival), safety, and translational research endpoints. Patients must meet these criteria: ≥ 18 yrs old; HLA-A*02:01, *02:05 or *02:06 positive; have advanced (metastatic or inoperable) MRCLS expressing NY-ESO-1 at 2+/3+ intensity in ≥30% of tumor cells by IHC; measurable disease; prior systemic anthracycline therapy; have ECOG status 0 or 1; and adequate organ function. Initially, ten patients are planned to be enrolled, with potential to enroll an additional 5 patients. Patients who do not receive the minimum cell dose or who do not receive the T-cell infusion may be replaced. Following apheresis, the T cells are isolated and expanded with CD3/CD28 beads, transduced with a lentiviral vector containing the NY-ESO-1c259 TCR, and 1– 8 × 10⁹ transduced T-cells are infused intravenously on Day 1 after lymphodepletion with fludarabine 30 mg/m²/day and cyclophosphamide 600 mg/m²/day on days -7 to -5. Response is assessed at 4, 8, 12 and 24 weeks, and then every 3 months until confirmation of progression of disease. On study tumor biopsies and blood samples will be evaluated to compare the pre- and post-T cell infusion immune profile for association with treatment outcome. Clinical trial information: NCT02992743