E7 T-cell Receptor (TCR) -T Cell Induction Therapy for Locoregionally Advanced HPV-associated Cancers

Inclusion Criteria: Histologically confirmed carcinoma of a primary tumor site and stage indicated in Table 3 of the protocol. Tumor with HPV16 genotype as determined by testing performed in a Clinical Laboratory Improvement Amendments (CLIA) certified laboratory. HLA haplotype that demonstrates the HLA-A*02:01 allele as determined by testing performed in a CLIA certified laboratory. Participants may be enrolled based on low resolution typing (i.e., HLA-A*02) but the HLA-A*02:01 allele type must be confirmed prior to apheresis. Measureable disease per RECIST Criteria Version 1.1 or PERCIST. Age > 18 years. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 at screening. Negative pregnancy test for women under 55 and all women who have had a menstrual period in the last 12 months. A pregnancy tests is not required for women who have had a bilateral oophorectomy or hysterectomy. Women of child-bearing potential must agree to use adequate contraception (i.e., intrauterine device, hormonal barrier method of birth control; abstinence; tubal ligation or vasectomy) prior to study entry and for four months after treatment. Should a women become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately. Seronegative for HIV antibody, hepatitis B surface antigen (sAg), and hepatitis C antibody. If a hepatitis C antibody test is positive, then testing for antigen by reverse transcription polymerase chain reaction (RT-PCR) must be negative. Participants must have organ and marrow function as defined below: Leukocytes > 3,000/Mantle cell lymphoma (mcL) Absolute neutrophil count > 1,500/mcL Platelets > 100,000/mcL Hemoglobin > 9.0 g/dL Total bilirubin within normal institutional limits except in participants with Gilbert's Syndrome who must have a total bilirubin < 3.0 mg/dL. Serum aspartate aminotransferase (AST) (SGOT)/ alanine transaminase (ALT)(SGPT) < 2.5 x upper limit of normal (ULN) Calculated creatinine clearance (CrCl) >50 mL/min/1.73 m2for participants with creatinine levels above institutional normal (by the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation). international normalized ratio (INR) or activated partial thromboplastin time ( aPTT) ≤1.5 X ULN unless the subject is receiving anticoagulant therapy. Subjects on anticoagulant therapy must have a PT or aPTT within therapeutic range and no history of severe hemorrhage. Participants must be able to understand and be willing to sign the written informed consent document. Participants must agree to participate in protocol CINJ 192103 (Pro2021002307) for gene therapy long term follow up and in protocol Cancer Institute of New Jersey (CINJ) 192002 (Pro2021000281) for biospecimen collection study.