Inclusion Criteria:

• Capable of giving signed informed consent including compliance with the requirements and restrictions listed in the informed consent form (ICF) and in the protocol. For participants <18 years of age (or the legal minimum age in the relevant country) their legal guardian must give informed consent. Pediatric participants will be included in age-appropriate discussion in order to obtain assent.
• Participant must be ≥ 10 years of age at the time of signing the informed consent. Participant scheduled to receive clinical drug product supply must also weigh ≥ 40 kg. For participant scheduled to receive commercial drug product supply and weighing < 40kg, the Investigator must also consult with the Medical Monitor prior to inclusion.
• Participant has a diagnosis of synovial sarcoma or myxoid/round cell liposarcoma, confirmed by local histopathology and with evidence of translocation per below: – for synovial sarcoma, 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)) is required; – for myxoid/round cell liposarcoma, the presence of a translocation t (12;16)(q13;p11) or the variant translocation t (12;22)(q13;q12) is required.
• Participant has high-risk locally advanced (i.e. deeply seated, high grade, positive margins, large [≥5 cm], or locally recurrent) synovial sarcoma or myxoid/round cell liposarcoma.
• Participant with synovial sarcoma or myxoid/round cell liposarcoma who is:
  • Newly diagnosed, previously untreated; OR
  • Relapsed after surgery or radiotherapy for localized disease; OR
  • Relapsed 1 year after adjuvant/neoadjuvant therapy for localized disease.
• Male or female. Contraception requirements will apply at the time of leukapharesis and treatment.A representative tumor tissue specimen (archived or fresh biopsy) with associated pathology report should be available to perform NY-ESO-1 antigen expression analysis, unless a recent NY-ESO-1 expression test result from the same designated central laboratory, following the same procedures, has already been performed under a separate GSK-sponsored protocol or under another substudy. 

All the Inclusion Criteria in 1-7 must apply again prior to leukapheresis. In addition, the following criteria must also apply:

• Life expectancy ≥ 24 weeks.
• Participant has advanced (metastatic or unresectable) synovial sarcoma or myxoid/round cell liposarcoma. Unresectable refers to a tumor lesion in which clear surgical excision margins cannot be obtained without leading to significant functional compromise.
• Participant must be positive for HLA-A*02:01, HLA-A*02:05, and/or HLA-A*02:06 alleles by a validated test in a designated central lab prior to leukapheresis.
  • NOTE: An HLA test result from the same designated central laboratory, following the same procedures, and performed under a separate GSK-sponsored protocol or under another substudy is acceptable.
• Participant’s tumor has been pathologically reviewed by a designated central laboratory with confirmed positive NY-ESO-1 expression defined as:
  • 30% of cells that are 2+ or 3+ by immunohistochemistry.
  • NOTE: A NY-ESO-1 expression test result from the same designated central laboratory, following the same procedures, and performed under a separate GSKsponsored protocol or under another substudy is acceptable.
• Left ventricular ejection fraction ≥ 45% with no evidence of clinically significant pericardial effusion.
• Performance status: for participants 60, or for participants < 16 and Lansky > 60, or for participants ≥ 16 and < 18 years of age, Karnofsky > 60, or for participants or for participants ≥ 18 years of age, Eastern Cooperative Oncology Group (ECOG) of 0-1.
• Participant must have adequate organ function and blood cell counts, within 7 days prior to the day of leukapheresis procedure (or first day of lymphodepletion during Treatment fitness assessment), as indicated by the following laboratory values.
• Hematological
• Absolute Neutrophil count (ANC) ≥1.5 x10^9 /L (without granulocute coloty-stimulating support);
• Absolute Lymphocyte count (ALC) ≥ 0.5 x 10^9 /L;
• Hemoglobin ≥ 8 g/dL or ≥ 5.6 mmol/L.
• Platelets ≥ 100 x10^9 /L (not achieved by transfusion).
• Creatinine clearance ≥ 40 mL/min.
• Participants who are ≥ 18 and < 65 years of age must be assessed either:
  • by 24-hour urine creatinine collection; OR
  • by using Serum Creatinine (Scr) via an estimated creatinine clearance calculated as below: Step 1: estimated glomerular filtration rate (GFR) to be obtained from the Chronic kidney disease Epidemiology Collaboration (CKD-EPI) formula [Levey, 2009]:
  • Estimated GFR (mL/min/1.73m^2 ) = 141 × min(Scr/κ, 1), α × max(Scr/κ, 1)-1.209 × 0.993Age × 1.018 [if female] × 1.159 [if black] where:
  • Scr is serum creatinine in mg/dL, κ is 0.7 for females and 0.9 for males, α is -0.329 for females and -0.411 for males, min(Scr/κ,1) indicates the minimum of Scr/κ or 1, max(Scr/κ,1) indicates the maximum of Scr/κ or 1, and Age is in years.
  • Step 2: correction factor to be applied per the American National Kidney Foundation in order to obtain the estimated creatine clearance in mL/min Estimated CrCl (mL/min) = Estimated GFR (mL/min/1.73 m^2 ) × BSA (m2 ) / 1.73 m^2.
• Participants ≥ 65 years of age must have renal function measured either by 24-hour urine creatinine collection or by nuclear medicine EDTA GFR measurement, according to standard practice at the treating institution.  Participants <18 years of age must have renal function measured either by 24-hour urine creatinine collection or by nuclear medicine EDTA GFR measurement or by serum creatinine collection, according to standard practice at the treating institution.
• Participants < 18 years of age must have GFR ≥ 70mL/min/1.73m^2 OR have a serum creatinine based on age/gender as follows:
  • Age Maximum serum creatinine (mg/dL) Male Female
  • Age 10 to < 13 years > 1.2
  • Age 13 to < 16 years > Male 1.5  | Female 1.4
  • Age 16 to < 18 years > Male 1.7 | Female 1.4
• Hepatic
• Total bilirubin
• Participants with Gilbert’s Syndrome (only if direct bilirubin ≤ 35%) | ≤ 1.5 x ULN (isolated bilirubin ≤ 1.5 x ULN is acceptable if bilirubin is fractionated and direct bilirubin < 35%)
• ALT ≤ 2.5 x ULN (or ≤ 5 x ULN if documented history of liver metastases)
• Coagulation
• International normalized ratio (INR) OR prothrombin time (PT)
• Activated partial thromboplastin time (aPTT) ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants Nutritional status.
• Albumin ≥ 3.5 g/dL
  • Participants may be transfused or receive growth factor treatment to meet minimum hematologic values up to 7 days prior to determining eligibility;
  • Adequate Organ Function will be reassessed for eligibility prior to lymphodepletion: if, upon consultation with the Medical Monitor, there is evidence from laboratory values that recovery from last anti-cancer treatment is underway, hematology labs may be considered acceptable and requirements waved to proceed with lymphodepletion.
• Participant is fit for leukapheresis and has adequate venous access for the cell collection.
• Male or female. Contraceptive use by men or women should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies.
• Male Participants: Male participants are eligible to participate if they agree to the following during the intervention period starting at the first dose of chemotherapy for at least 12 months after receiving the T-cell infusion, or 4 months after there is no evidence of persistence/ gene modified cells in the participant’s blood, whichever is longer. Refrain from donating sperm Plus, either: Be abstinent from heterosexual or homosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis) and agree to remain abstinent OR Must agree to use contraception/barrier as detailed below:
  • Agree to use a male condom and should also be advised of the benefit for a female partner to use a highly effective method of contraception when having sexual intercourse with a woman of childbearing potential (WOCBP) who is not currently pregnant (as a condom may break or leak);
  • Agree to use male condom when engaging in any activity that allows for passage of ejaculate to another person.
• Female Participants: A female participant is eligible to participate if she is not pregnant or breastfeeding, and at least one of the following conditions applies:
  • Is not a WOCBP; OR
  • Is a WOCBP who will agree to use a barrier method (male condom) and use a contraceptive method that is highly effective (with a failure rate of < 1% per year) during the intervention period and for at least 12 months after receiving the T-cell infusion, or 4 months after there is no evidence of persistence/ gene modified cells in the participant’s blood, whichever is longer.  WOCBP should also agree not to donate eggs (ova, oocytes) for the purpose of reproduction during this period. The Investigator should evaluate the effectiveness of the contraceptive method in relationship to the first dose of study intervention.
  • A WOCBP must have a negative highly sensitive pregnancy test (urine or serum as required by local regulations) within 24 hours before any dose of study intervention. If a urine test cannot be confirmed as negative (e.g., an ambiguous result), a serum pregnancy test is required. In such cases, the participant must be excluded from participation if the serum pregnancy result is positive. The Investigator is responsible for review of medical history, menstrual history, and recent sexual activity to decrease the risk for inclusion of a woman with an early undetected pregnancy.
• Female participants of childbearing potential (FCBP) must have a negative urine or serum pregnancy test.
• Safety assessments will be reassessed again prior to lymphodepletion. Treatment fitness will be established in consultation with Medical Monitor.

In addition, the following criteria must also apply:

• Participant has measurable disease according to RECIST v1.1.
• Supportive radiotherapy has not affected > 25% of bone marrow.
• A biopsy (excisional, incisional, or core) of non-target tumor tissue obtained within 90 days prior to initiating lymphodepleting chemotherapy is mandatory if cleanically feasible. This biopsy will be used as baseline for biomarker analyses. If it is not feasible to obtain a fresh biopsy, an archival tumor tissue (FFPE block) taken after completion of the participant’s last line of therapy, preferably within 90 days prior to initiating lymphodepleting chemotherapy, may be accepted at the discretion of the Medical Monitor (or designee). For participants who already provided a fresh biopsy for antigen expression and did not receive any supportive or intermediate anti-cancer therapy, the screening biopsy will be used for baseline.

Exclusion Criteria:

• Participant has been previously treated for advanced (metastatic or unresectable) synovial sarcoma or myxoid/round cell liposarcoma.
• Central nervous system (CNS) metastases.
• Any other prior malignancy that is not in complete remission.
• Exceptions include:
  • completely resected non-melanoma skin cancer, or successfully treated in situ carcinoma (e.g., melanoma in situ, basal cell carcinoma, prostate cancer in-situ, periosteal osteosarcoma);
  • previous malignancies that have been definitively treated, and have been in remission for 5 years may be enrolled upon consultation with sponsor Medical Monitor or designee.
• Previous treatment with genetically engineered NY-ESO-1 specific T cells.
• Previous NY-ESO-1 vaccine or NY-ESO-1 targeting antibody.
• Prior gene therapy using an integrating vector.
• Previous allogeneic hematopoietic stem cell transplant.
• Clinically significant systemic illness: a. serious active infections or significant cardiac, pulmonary, hepatic or other organ dysfunction, that in the judgment of the Investigator would compromise the participant’s ability to tolerate protocol therapy or significantly increase the risk of complications; OR
• Prior or active demyelinating disease. Please note in particular that mandatory washout period restrictions must be respected before starting leukapheresis.

In addition, participants are not eligible for leukapharesis if any of the following criteria apply: 

• Participant has history of chronic or recurrent (within the last year prior to leukapheresis) severe autoimmune or immune mediated disease (e.g., Crohn’s disease, systemic lupus) requiring steroids or other immunosuppressive treatments.
• Uncontrolled intercurrent illness including, but not limited to:
  • Ongoing or active infection;
  • Clinically significant cardiac disease defined by congestive heart failure New York Heart Association (NYHA) Class 3 or Class 4;
  • Uncontrolled clinically significant arrhythmia;
  • Acute coronary syndrome (angina or myocardial infarction) in last 6 months;
  • Interstitial lung disease (participants with existing pneumonitis as a result of radiation are not excluded; however, participants cannot be oxygen dependent).
• Current active liver or biliary disease (with the exception of Gilbert’s syndrome or asymptomatic gallstones, liver metastases or otherwise stable chronic liver disease per Investigator assessment).
  • NOTE: Stable chronic liver disease should generally be defined by the absence of ascites, encephalopathy, coagulopathy, hypoalbuminemia, oesophageal or gastric varices, persistent jaundice or cirrhosis.
• QTc > 480 msec.
  • NOTES: The QTc is the QT interval corrected for heart rate according to Bazett’s formula (QTcB), Fridericia’s formula (QTcF), and/or another method, machine-read or manually over-read. The specific formula that will be used to determine eligibility for an individual participant should be determined prior to initiation of the study. In other words, several different formulae cannot be used to calculate the QTc for an individual participant and then the lowest QTc value used to include or discontinue the participant from the trial. For purposes of data analysis, QTcB, QTcF, another QT correction formula, or a composite of available values of QTc will be used as specified in the Reporting and Analysis Plan (RAP).
• Participant has a history of allergic reactions attributed to compounds of similar chemical or biologic composition to cyclophosphamide, fludarabine, other agents used in the study.
• Pregnant or breastfeeding females (due to risk to fetus or newborn).
• Any prior treatment-related toxicities must be CTCAE (Version 5.0) ≤ Grade 1 at the time of initiating study intervention (except for non-clinically significant toxicities e.g., alopecia, vitiligo). Participants with Grade 2 toxicities that are deemed stable or irreversible (e.g., chemotherapy related arthritis or tendinitis, skin discoloration or erythema) can be enrolled.
• Other standard of care lines of therapy are allowed only if guidelines and washout periods.
• Investigational treatment within 30 days or 5 half-lives (whichever is shorter) prior to leukapheresis. Investigational vaccines (other than NY-ESO-1 vaccines that are not allowed) must follow the washout period. Exceptions to this rule must be evaluated by the Investigator in agreement with the Sponsor’s Medical Monitor (or designee).
• Participant has active infection with HIV, HBV, HCV, EBV, CMV, syphilis, or HTLV as defined below:
  • Positive serology for HIV;
  • Active hepatitis B infection as demonstrated by test for hepatitis B surface antigen. Participants who are hepatitis B surface antigen negative but are hepatitis B core antibody positive must have undetectable hepatitis B DNA and receive prophylaxis against viral reactivation;
  • Active hepatitis C infection as demonstrated by hepatitis C RNA test. Participants who are HCV antibody positive will be screened for HCV RNA by any RT PCR or bDNA assay. If HCV antibody is positive, eligibility will be determined based on a negative Screening RNA value;
  • Positive test for syphilis (spirochete bacterium);
  • Positive serology for HTLV 1 or 2.
• Has known psychiatric or substance abuse disorders that would interfere with cooperating with the requirements of the study. Treatment fitness will be established in consultation with Medical Monitor. Please note in particular that mandatory washout period restrictions must be respected before starting lymphodepletion.

In addition, participants cannot proceed with lymphodepletion or treatment if any of the following criteria apply:

• Participant has received cytotoxic therapy within 3 weeks prior to lymphodepleting chemotherapy.
• Systemic corticosteroids or any other immunosuppressive therapy within 2 weeks prior to lymphodepleting chemotherapy.
  • NOTE: Isolated doses of systemic corticosteroids are permitted to manage acute allergic reactions. Use of inhaled or topical steroids is not exclusionary.
• Participant has received radiotherapy to the target lesions within 3 months prior to lymphodepletion. A lesion with unequivocal progression may be considered a target lesion regardless of time from last radiotherapy dose.
  • NOTE: There is no washout period for palliative radiation to non-target lesions.
• Participant has received an anti-cancer vaccine within 2 months in the absence of tumor response. The participant should be excluded if their disease is responding to an experimental vaccine given within 6 months.
• Participant has received live vaccine within 4 weeks prior to lymphodepletion or intends to receive live vaccine during the 3 month period following administration of GSK3377794.
• Participant has received immune therapy (monoclonal antibody therapy, checkpoint inhibitors) within 4 weeks of lymphodepletion.
• Participant had major surgery ≤ 28 days of first dose of study intervention.