ADP-A2M4CD8 Monotherapy and in Combination With Nivolumab in HLA-A2+ Subjects With MAGE-A4 Positive Ovarian Cancer (SURPASS-3)

Inclusion Criteria: Subjects will be assessed for eligibility prior to leukapheresis AND prior to lymphodepleting chemotherapy (unless otherwise noted) and must meet all specified criteria for study participation. Inclusion Criteria: Subject (or legally authorized representative) has voluntarily agreed to participate by giving written informed consent in accordance with International Council for Harmonisation (ICH) Good Clinical Practice (GCP) guidelines and applicable local regulations. Subject (or legally authorized representative) has agreed to abide by all protocol-required procedures including study related assessments and management by the treating institution for the duration of the study, including LTFU. Subject is ≥ 18 and ≤ 75 years of age at the time the Pre Screening informed consent form (ICF) is signed. Subject has histologically confirmed diagnosis of high-grade serous or high-grade endometrioid recurrent ovarian carcinoma, including primary peritoneal and fallopian tube carcinoma. Subject has measurable disease according to RECIST v1.1 prior to lymphodepletion. Measurable disease is not required prior to leukapheresis. Subject has the following disease-specific prior therapy requirements: The initial therapy must have included at least 3 cycles of a prior platinum and taxane based chemotherapy regimen for primary disease, possibly including intraperitoneal therapy, consolidation, or extended therapy (maintenance/consolidation). Subjects may receive up to 4 prior regimens of combination or single agent systemic treatment for recurrent or metastatic disease, which may include investigational therapies unless discussed and agreed upon with the Sponsor or designee. Subjects who have received only 1 line of platinum based therapy must have progressed between 93 and 183 days of completing platinum based therapy as a part of front line treatment of ovarian cancer. Subjects who have progressed within 92 days of completing platinum based therapy in front line treatment are excluded. Subjects who have received 2 or more lines of platinum based therapy must have progressed during or within 183 days of completing the latest platinum based therapy for treatment of recurrent ovarian cancer. The number of days (platinum-free interval) should be calculated from the date of the last administered dose of platinum therapy to the date of documentation of progression. Subjects with a known BRCA mutation (germ line or somatic) must have received a poly adenosine diphosphate-ribose polymerase (PARP). Subjects must have received bevacizumab. Positive for HLA-A*02:01, HLA-A*02:02, HLA-A*02:03, or HLA-A*02:06 allele as determined by Adaptimmune-designated central laboratory testing. HLA-A*02 alleles having the same protein sequence in the peptide binding domains (P group) will also be included. Other HLA-A*02 alleles may be eligible after adjudication with the Sponsor. MAGE-A4 expression, defined as ≥ 30% of tumor cells that are ≥ 2+ by IHC, should be documented at the pre screening period based on either an archival specimen or a fresh biopsy. All samples must have been pathologically reviewed by an Adaptimmune-designated central laboratory confirming expression. Subject has an Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 or 1. Subject has left ventricular ejection fraction (LVEF) of ≥ 50% or the institutional lower limit of normal range, whichever is lower. Subject is fit for leukapheresis, and adequate venous access can be established for the cell collection. Subjects of childbearing potential must have a negative urine or serum pregnancy test AND must agree to use a highly effective method of contraception starting at the first dose of chemotherapy and continue for at least 12 months or for 4 months after the gene-modified cells are no longer detected in the blood, or 6 months after the last dose of nivolumab, whichever is longer. Subjects of childbearing potential must also agree to refrain from egg donation, storage, or banking during these same time periods. Subjects must have ≥ 90% room air oxygen saturation test at rest at Screening (within 7 days of leukapheresis) and at Baseline. Subject must have adequate organ function as indicated by the laboratory values in the table below. System Laboratory Value Hematological Absolute neutrophil count (ANC) ≥ 1.5 × 109/L (without granulocyte colony stimulating factor [G-CSF] support) Platelets ≥ 100 × 109/L (without transfusion support within 5 days prior to leukapheresis and lymphodepletion) Hemoglobin (Hb) ≥ 90 g/L (without transfusion support within 5 days prior to leukapheresis and lymphodepletion) Coagulation Prothrombin time or international normalized ratio (INR) ≤ 1.5 × upper limit of normal (ULN), unless receiving therapeutic anticoagulation Partial thromboplastin time ≤ 1.5 × ULN, unless receiving therapeutic anticoagulation Renal Glomerular filtration rate (GFR) or creatinine clearance (CrCl) (estimated or calculated)1 ≥ 50 mL/min /1.73 m2 or ≥ 50 mL/min Hepatic Serum total bilirubin ≤ 1.5 × ULN (unless subject has documented Gilbert's Syndrome with direct bilirubin < 35% of total bilirubin) Exception: Subjects with liver metastasis ≤ 2.5 × ULN Alanine aminotransferase (ALT) / Aspartate aminotransferase (AST) ≤ 2.5 × ULN Exception: Subjects with liver metastasis ≤ 5.0 × ULN 1 Renal function (GFR or CrCl) will be estimated or measured according to standard practice at the treating institution. Renal function will be reassessed at Baseline using the same methodology. Note: Laboratory values that are slightly out of the laboratory test parameters, if assessed as not clinically significant by the site study Investigator, may be acceptable after discussion and review by the Sponsor Study Physician. This applies to screening laboratory assessments and baseline laboratory assessments. Exclusion Criteria: Positive for HLA-A*02:05 in either allele as determined by Adaptimmune-designated central laboratory testing. HLA-A*02 alleles having the same protein sequence as HLA-A*02:05 in the peptide binding domains (P groups) will also be excluded. Other alleles may be exclusionary after adjudication with the Sponsor. Subject has received or plans to receive the following therapy/treatment prior to to leukapheresis or lymphodepleting chemotherapy, unless stopped according to the washout requirements: Toxicity from previous anti-cancer therapy that has not recovered to Grade ≤ 1 or baseline prior to enrollment (except for nonclinically significant toxicities, e.g., alopecia and vitiligo). Subjects with Grade 2 toxicities that are deemed stable or irreversible (e.g., peripheral neuropathy) can be enrolled. Subject has a history of allergic reactions attributed to compounds of similar chemical or biological composition to fludarabine, cyclophosphamide, or other agents used in the study. Subject has an active autoimmune or immune-mediated disease that has not yet been resolved. Subjects with immune-mediated AEs secondary to treatment with immunotherapy that resolve to Grade ≤ 1 off steroids are permitted. Subjects with hypothyroidism, type I diabetes, adrenal insufficiency, or pituitary insufficiency that are stable on replacement therapy are eligible. Subjects with disorders such as asthma, vitiligo, psoriasis, or atopic dermatitis that are well controlled without requiring systemic immunosuppression are also eligible. Other stable immune conditions that do not require prednisone > 20 mg/day (or its equivalent for other corticosteroid agents) may be acceptable with the agreement of the Sponsor. Subject had major surgery within 4 weeks prior to lymphodepletion; subjects should have been fully recovered from any surgical-related toxicities. Surgical-related toxicities that are not clinically significant per Investigator assessment may be acceptable after discussion and agreement with the Study Physician. Leptomeningeal disease, carcinomatous meningitis, or symptomatic central nervous system (CNS) metastases. Subjects with prior history of symptomatic CNS metastases must have received treatment (i.e., SRS, WBRT, or surgery) and be neurologically stable for at least 1 month, not requiring anti-seizure medications, or off steroids for at least 14 days prior to leukapheresis and lymphodepletion. Subjects who have asymptomatic CNS metastases without associated edema, shift, or requirement for steroids or anti-seizure medications are eligible. If such a subject receives SRS or WBRT, a minimum period of 2 weeks needs to lapse between the therapy and lymphodepletion. Prophylactic anti-seizure medication is allowed. Subject has any other prior malignancy that is not considered by the Investigator to be in complete remission. Resectable squamous or basal cell carcinoma of the skin is acceptable. Prior malignancies that have been surgically resected and show no evidence of disease are acceptable. Clinically significant cardiovascular disease including, but not limited to, any of the following: Electrocardiogram (ECG) showing clinically significant abnormality at Screening Uncontrolled clinically significant arrhythmias Known family history or congenital history of prolonged QT syndrome or history of torsade de pointes Uncontrolled hypertension despite optimal medical therapy Acute coronary syndrome (angina or myocardial infarction) in the last 6 months Clinically significant cardiac disease defined by congestive heart failure New York Heart Association Class 3 and 4 History of stroke, CNS bleeding, transient ischemic attack, or reversible ischemic neurologic deficit within last 6 months Uncontrolled intercurrent illness including, but not limited to, any of the following: Ongoing or active systemic infection, or localized infection which may become systemic due to leukapheresis procedure, e.g., catheter insertion will be excluded. Subjects with urinary tract infections will be included only following treatment with antibiotics.(For SARS-CoV 2 [COVID-19] infection, see Section 10.4.4.1) Clinically significant pulmonary disease with any 1 pulmonary function parameter < 60% predicted (forced expiratory volume first forced breath [FEV1], total lung capacity [TLC], or diffusing capacity of lungs for carbon monoxide [DLCO]; note: for patients with anemia, corrected DLCO could be used) assessed prior to leukapheresis and within 2 months of the start of lymphodepleting chemotherapy Requirement for oxygen support (due to cardiac or pulmonary disease) Interstitial lung disease (pneumonitis) or history of pneumonectomy or chronic obstructive pulmonary disease with ≥ 1 exacerbation within 1 year prior to the Screening Visit that required treatment with systemic corticosteroids or resulted in hospitalization Hospitalization for bowel obstruction in last 2 months Hematosis or significant organ bleeding in last 2 months Ascites or pleural effusion which requires repeated (2 within 4 weeks) paracentesis or thoracentesis within last 2 months Cardiac or pericardial tumor involvement (prior to lymphodepletion) Active infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV), hepatitis C virus (HCV), or human T cell leukemia virus (HTLV) as defined below. Re-screening for infectious disease markers is not required at baseline (prior to lymphodepletion) unless > 6 months has elapsed. Positive serology for HIV Active hepatitis B infection as demonstrated by test for hepatitis B surface antigen. Subjects 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. Prophylaxis should be initiated prior to lymphodepleting therapy and continued for 6 months. Active hepatitis C infection as demonstrated by hepatitis C ribonucleic acid (RNA) test. Subjects who are HCV antibody-positive will be screened for HCV RNA by any reverse transcription-polymerase chain reaction (RT PCR) or branched DNA (bDNA) assay. If HCV antibody is positive, eligibility will be determined based on a negative screening RNA value. Positive serology for HTLV 1 or 2 Subject is pregnant or breastfeeding. Subjects who have illicit drug or alcohol dependency within the past year. In the opinion of the Investigator, subject will be unlikely to fully comply with protocol requirements. Intolerance to nivolumab includes severe allergic reaction to nivolumab or any components (active or inactive) of nivolumab.