Autologous T Cells Targeting HPV16 HPV18 & Survivin in Patients With R/R HPV-related Oropharyngeal Cancers

Inclusion Criteria: 1. The patient will be typed for HLA-A\*0201 expression as determined by high resolution sequence-based typing method. If documented HLA results are available from a previous test, the patient can be enrolled using these results after review and approval by the sponsor. 2. Patients with cytologically or histologically confirmed locally advanced or metastatic HPV related oropharyngeal cancers with confirmed detection of HPV-16 and/or HPV-18. 3. Patients with HPV-related oropharyngeal cancers who have received at least 1 prior line of standard-of-care (SOC) treatment (for example, per the current NCCN Guidelines for Patients with Oropharyngeal Cancer) consisting of systemic immunotherapy and/or chemotherapeutic treatment. 1. The last dose of cytotoxic chemotherapy and/or steroids must be administered at least 28 days prior to the leukapheresis procedure. 2. Any adverse event(s) that the patient may have experienced from prior therapy must have resolved to ≤ Grade 1 according to NCI CTCAE version 5.0. 4. Measurable disease per RECIST v1.1 criteria (at least 1 lesion that can be measured accurately in at least 1 dimension with the longest diameter ≥ 10 mm \[MRI or CT scan sliced thickness ≤ 5 mm\]). 5. Pulse oximetry ≥ 92% on room air. 6. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. 7. Life expectancy of at least 3 months. 8. Be willing to comply with the study schedule and all other protocol requirements. 9. Women of childbearing potential (WOCBP), defined as a sexually mature woman who has not undergone a hysterectomy or tubal ligation or who has not been naturally postmenopausal for at least 24 consecutive months, must have 2 negative pregnancy tests prior to treatment. All sexually active WOCBP and all sexually active male patients must agree to use highly effective methods of birth control throughout the study. 10. Ability of the patient to understand and willingness to sign a written informed consent form. Exclusion Criteria: 1. A diagnosis of other malignancies if the malignancy has required therapy within the last 3 years or is not in complete remission. Exceptions are non-metastatic basal cell or squamous cell carcinomas of the skin or prostate cancer that does not require treatment. Patients taking adjuvant hormonal therapy for definitively treated cancers (e.g., breast cancer, prostate cancer) are eligible. 2. Major surgery within 28 days prior to the first study drug administration (minimally invasive procedures, such as diagnostic biopsies, are permitted). 3. Known central nervous system involvement. 4. Treatment with an allogeneic hematopoietic stem cell transplantation. 5. Treatment with any investigational agent(s) at the time of informed consent. 6. Left ventricular ejection fraction (LVEF) \< 45%, congestive heart failure (as defined by New York Heart Association Functional Classification III or IV), unstable angina, serious uncontrolled cardiac arrhythmia, a myocardial infarction within 6 months prior to study entry or a history of myocarditis. 7. The following hematological laboratory results at Screening (these results must be independent of blood product or hematopoietic growth factor support): 1. Hemoglobin \< 9.0 g/dL. 2. Platelet count \< 100,000/μL. 3. Absolute neutrophil count (ANC) \< 1000/ μL. 8. The following chemistry laboratory results at Screening: 1. Serum creatinine ≥ 1.5 mg/dL or estimated glomerular filtration rate (eGFR) ≤ 50 mL/min/1.73 m\^2. 2. Serum aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \> 3x the upper limit of normal (ULN) or serum total bilirubin \> 2 mg/dL (except for patients in whom hyperbilirubinemia is attributed to Gilbert's Syndrome). 9. International normalized ratio (INR) or activated partial thromboplastin time (aPTT) \> 1.5x ULN within 1 week prior to the start of lymphodepletion chemotherapy, unless on a stable dose of an anticoagulant. 10. Are pregnant or breastfeeding. 11. Vaccination with any live virus vaccine is not permitted prior to the initiation of study treatment. 1. Inactivated annual influenza vaccination is allowed. 2. Vaccines such as COVID-19 vaccine, e.g., SARS-CoV-2 vaccine \> 7 days before administration is acceptable. For vaccines requiring more than 1 dose, the full regimen should be completed prior to Cycle 1 Day 1. 12. Active bacterial, viral, or fungal infection within 72 hours of the start of lymphodepletion chemotherapy; patients with ongoing use of prophylactic antibiotics, antifungal agents, or antiviral agents remain eligible as long as there is no evidence of active infection. 13. Have human immunodeficiency virus (HIV) active infection as indicated by positive HIV polymerase chain reaction (PCR) test, human T-cell leukemia virus type 1 infection, or hepatitis B virus (HBV) or hepatitis C virus (HCV) viremia or are at risk for HBV reactivation (at risk for HBV reactivation is defined as being hepatitis B surface antigen \[HbsAg\] positive, or anti-HBe-antibody positive), or are positive for HBV DNA. HCV ribonucleic acid (RNA) must be undetectable by laboratory test. 14. Any condition including the presence of laboratory abnormalities, that places the patient at an unacceptable risk if the patient was to participate in the study. 15. Have an active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids, or immunosuppressive drugs). Note: Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is permitted. 16. Patients who experienced the following immune checkpoint inhibitor-related AEs even if the AE resolved to ≤ Grade 1 or baseline: 1. ≥ Grade 3 ocular AE 2. Changes in liver function tests that met the criteria for Hy's Law (\> 3× ULN of either ALT/AST with concurrent \> 2× ULN of total bilirubin (total and direct) and without alternate etiology) 3. ≥ Grade 3 neurologic toxicity 4. ≥ Grade 3 colitis 5. ≥ Grade 3 renal toxicity