This Phase 1 study is designed as a cell dose escalation trial in HLA-A*02:01 and HLA-A*02:06 subjects with MAGE-A10 positive urothelial, melanoma or head and neck tumors. The study will enroll subjects between the ages of 18 and 75 using a modified 3+3 cell dose escalation design, to evaluate dose limiting toxicities and determine the target cell dose range. Following the dose escalation phase, additional subjects will be enrolled at the target cell dose range to further characterize safety and the effects at this cell dose.

The study will take the subject's T cells, which are a natural type of immune cell in the blood, and send them to a laboratory to be modified. The changed T cells used in this study will be the subject's own T cells that have been genetically changed with the aim of attacking and destroying cancer cells. When the MAGE-A10ᶜ⁷⁹⁶T cells are available, subjects will undergo lymphodepleting chemotherapy with cyclophosphamide and fludarabine, followed by T cell infusion. The purpose of this study is to test the safety of genetically changed T cells and find out what effects, if any, they have in subjects with urothelial, melanoma or head and neck cancer.

Subjects will be seen frequently by the Study Physician after receiving their T cells for the next 6 months. After that, subjects will be seen every 3, 6, or 12 months according to the Schedule of Procedures. All subjects completing or withdrawing from the interventional portion of the study will enter a long term follow-up phase for observation of delayed adverse events and overall survival for 15 years post-infusion.

Inclusion Criteria:

1. Subject is ≥18 to ≤75 years of age at the time of signing the study informed consent.
2. Subject has histologically confirmed diagnosis of any one of the following cancers: (A) urothelial cancer (transitional cell cancer of the bladder, ureter or renal pelvis), (B) melanoma, or (C) squamous cell carcinoma of the head and neck.
3. Subject is HLA-A*02:01 and/or HLA-A*02:06 positive.
4. Subject has measurable disease according to RECIST v1.1 criteria prior to lymphodepletion
5. Subject meets disease-specific requirements per protocol
6. Subject has anticipated life expectancy > 6 months prior to leukapheresis and >3 months prior to lymphodepletion.
7. Subject's tumor shows positive MAGE-A10 expression
8. Subject has an Eastern Cooperative Oncology Group (ECOG) Performance Status 0-1.
9. Subject has a left ventricular ejection fraction ≥50%.
10. Subject is fit for leukapheresis and has adequate venous access for the cell collection.
11. Female subject of childbearing potential (FCBP) must have a negative urine or serum pregnancy test or male subject must be surgically sterile or agree to use a double barrier contraception method or abstain from heterosexual activity with a female of childbearing potential starting at the first dose of chemotherapy and for 4 months thereafter.
12. Subject must have adequate organ function per protocol

Exclusion Criteria:

1. Subject is HLA-A*02:05 in either allele, HLA-B*15:01 and/or HLA-B*46:01 positive. Subject has any A*02 null allele (designated with an "N", e.g. A*02:32N) as the sole HLA-A*02 allele.
2. Subject has received or plans to receive excluded therapy/treatment prior to leukapheresis or lymphodepleting chemotherapy per protocol
3. Subject that has toxicity from previous anti-cancer therapy must have recovered to ≤ Grade 1 prior to enrollment
4. Subject has history of allergic reactions attributed to compounds of similar chemical or biologic composition to fludarabine, cyclophosphamide or other agents used in the study.
5. Subject had major surgery within 4 weeks prior to lymphodepletion; subjects should have been fully recovered from any surgical related toxicities.
6. Subject has an electrocardiogram (ECG) showing clinically significant abnormality at Screening or showing an average QTc interval ≥450 msec in males and ≥470 msec in females (≥480 msec for subjects with bundle branch block [BBB]) over 3 consecutive ECGs. Either Fridericia's or Bazett's formula may be used to correct the QT interval.
7. Subject has symptomatic CNS metastases.
8. Subject has a history of chronic or recurrent severe autoimmune or immune mediated disease
9. Subject has any other active malignancy besides the tumor under study within 3 years prior to Screening.
10. Subject has uncontrolled intercurrent illness
11. Subject has active infection with HIV, HBV, HCV or HTLV
12. Subject is pregnant or breastfeeding.