Phase I/Ib Study of NK Expressing an Affinity-enhanced T-cell Receptor (TCR) Against the NY-ESO-1

Inclusion Criteria: 1. Patients with all cancer histology, with an HLA-A\*02:01, HLA-A\*02:05 or HLA-A\*02:06 positive and a positive expression of NY-ESO-1 (\>/= 50% tumor cells 2+ or 3+ by IHC) in the preenrollment tumor sample, for the dose escalation cohort. NY-ESO expression must be confirmed at MDACC prior to study entry. 2. Patients with histologically confirmed synovial sarcoma (cohort 1) or myxoid/round cell liposarcoma (cohort 2), with an HLA-A\*02:01, HLA-A\*02:05 or HLA-A\*02:06 positive and a positive expression of NY-ESO-1 (\>/= 50% tumor cells 2+ or 3+ by IHC) in the pre-enrollment tumor sample, for the expansion cohorts. Archival samples will be permitted for screening. NY-ESO expression must be confirmed at MDACC prior to study entry. 3. Patients must meet disease-specific eligibility criteria (see below). 4. Patients must have relapsed or become refractory to standard of care treatment and must have received at least one prior line of systemic therapy including either doxorubicin and/or ifosfamide (synovial sarcoma and MRCLS) or trabectedin (MRCLS). 5. Patients must have measurable disease per the RECIST v1.1 at enrollment. 6. Patients must be at least 2 weeks from last cytotoxic chemotherapy at the time of first administration of lymphodepleting chemotherapy. Patients may continue tyrosine kinase inhibitors or other targeted therapies until at least 3 days prior to administration of lymphodepleting chemotherapy. 7. Patients must be at least 3 months from any cell therapy for malignancy. 8. Eastern Cooperative Oncology Group performance status 0-1 (Appendix A). 9. Adequate organ function at screening, as defined by the following: 1. Renal: Serum creatinine ≤ 1.5 mg/dL or estimated glomerular filtration rate (Chronic Kidney Disease Epidemiology Collaboration equation) ≥45 ml/min/1.73 m2 2. Hepatic: alanine transaminase (ALT)/aspartate transaminase (AST) ≤ 2.5 x upper limit of normal (ULN) or ≤ 5 x ULN if documented liver metastases, total bilirubin ≤ 1.5 mg/dL or ≤ 3.0 mg/dL for patients with Gilbert's Syndrome. No history of liver cirrhosis and no ascites. 3. Cardiac: Cardiac ejection fraction ≥ 50%, no clinically significant pericardial effusion as determined by echocardiogram (ECHO) or multigated acquisition (MUGA) scan, and no symptomatic cardiac disease or history of serious ventricular arrhythmia (ie, ventricular tachycardia or ventricular fibrillation), high-grade atrioventricular block, or other cardiac arrhythmias requiring anti-arrhythmic medications (except for atrial fibrillation that is well controlled with anti-arrhythmic medication) 4. Pulmonary: No clinically significant pleural effusion (per principal investigator \[PI\] judgement), and baseline oxygen saturation ≥ 92% on room air, 5. Hematological: absolute neutrophil count (ANC) ≥ 1000/mm3, platelet count ≥ 75,000/mm3, and hemoglobin ≥ 8 g/dL 6. Coagulation: International normalized ratio (INR) ≤ 1.5 ULN and activated partial thromboplastin time (aPTT) ≤ 1.5 ULN. Patients on therapeutic doses of anticoagulation medication must have INR and/or aPTT ≤ the upper limit of the therapeutic range for intended use. 10. Able to provide written informed consent. 11. Aged 16-80 years. 12. Weight ≥40 kg. 13. All male and female patients who are able to have children must practice effective birth control while on study therapy and for up to 3 months post completion of study therapy. Acceptable forms of birth control for female patients include: hormonal birth control, intrauterine device, diaphragm with spermicide, condom with spermicide, or abstinence. Female patients who become pregnant or suspect pregnancy must immediately notify their doctor. Females patients who become pregnant will be taken off study. Men who are able to have children must use effective birth control while on the study therapy. Acceptable forms of birth control for male patients include: condom with spermicide or abstinence. If the male patient fathers a child or suspects that he has fathered a child while on the study, he must immediately notify his doctor. 14. Negative serum or urine beta human chorionic gonadotropin pregnancy test for females of childbearing potential (defined as not postmenopausal for 24 months or no previous surgical sterilization or lactating females) at screening. 15. Signed consent to long-term follow-up on protocol PA17-0483. 16. Disease-specific inclusion criteria 17. Advanced solid tumors a. Patients with locally advanced and/or metastatic solid tumors may be enrolled in the dose escalation phase. Patients must have received at least one prior line of standard therapy. 18 Synovial Sarcoma (SS) a. Patients must have a histologically confirmed diagnosis of synovial sarcoma with a confirmation by the presence of a translocation between SYT on the X chromosome and SSX1, SSX2 or, SSX4 on chromosome 18 (may be presented in the pathology report as t (X; 18)). 19\. Myxoid/round cell liposarcoma (MRCLS) a. Patients must have histologically confirmed myxoid/round cell liposarcoma with a confirmation by the presence of the reciprocal chromosomal translocation t(12;16)(q13;p11) or t(12; 22) (q13;q12). Exclusion Criteria: 1. Presence of clinically significant ≥ Grade 2 toxicity from previous anticancer treatment, as determined by the PI. 2. Presence of fungal, bacterial, viral, or other infection requiring IV antimicrobials for management or not responding to appropriate therapy. Note: Patients with simple urinary tract infection and uncomplicated bacterial pharyngitis are permitted if responding to active treatment. 3. Known Active hepatitis B or C. 4. Known human immunodeficiency virus with detectable viral load. 5. Presence of active neurological disorder(s). 6. Active autoimmune disease within 12 months of enrollment (excluding low-grade psoriasis or well-controlled autoimmune thyroid disease). 7. Amyloidosis or POEMS syndrome. 8. Symptomatic or uncontrolled central nervous system involvement