Immunotherapy Using Tumor Infiltrating Lymphocytes for Patients With Metastatic Human Papillomavirus-Associated Cancers

-INCLUSION CRITERIA: 1. Measurable metastatic or locally advanced refractory/recurrent malignancies that are human papilloma virus 16 (HPV-16) or human papilloma virus 18 (HPV-18) high HPV positive by in situ hybridization (ISH) or polymerase chain reaction (PCR) or any cancer from the uterine cervix.. 2. All patients must have received at least one standard chemotherapy or chemoradiotherapy. 3. Patients with 3 or fewer brain metastases that are less than 1 cm in diameter and asymptomatic are eligible. Lesions that have been treated with stereotactic radiosurgery must be clinically stable for 1 month after treatment for the patient to be eligible. 4. Greater than or equal to 18 years of age and less than or equal to age 70. 5. Able to understand and sign the Informed Consent Document 6. Clinical performance status of Eastern Cooperative Oncology Group (ECOG) 0 or 1. 7. Life expectancy of greater than three months 8. Patients of both genders must be willing to practice birth control from the time of enrollment on this study and for up to four months after treatment. 9. Serology: * Seronegative for human immunodeficiency virus (HIV) antibody. (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who are HIV seropositive can have decreased immune-competence and thus be less responsive to the experimental treatment and more susceptible to its toxicities.) * Seronegative for hepatitis B antigen, and seronegative for hepatitis C antibody. If hepatitis C antibody test is positive, then patient must be tested for the presence of antigen by reverse transcription - polymerase chain reaction (RT-PCR) and be hepatitis C virus ribonucleic acid (HCV RNA) negative. 10. Women of child bearing potential must have a negative pregnancy test because of the potentially dangerous effects of the treatment on the fetus. 11. Hematology * Absolute neutrophil count greater than 1000/mm(3) without the support of filgrastim * White blood cell (WBC) greater than or equal to 3000/mm(3) * Platelet count greater than or equal too 100,000/mm(3) * Hemoglobin greater than 8.0 g/dl 12. Chemistry: * Serum alanine aminotransferase (ALT)/aspartate aminotransferase (AST) less than or equal to to 2.5 times the upper limit of normal * Serum creatinine less than or equal to to 1.6 mg/dl * Total bilirubin less that or equal to 1.5 mg/dl, except in patients with Gilbert's Syndrome who must have a total bilirubin less than 3.0 mg/dl. 13. More than four weeks must have elapsed since any prior systemic therapy at the time the patient receives the preparative regimen, and patients toxicities must have recovered to a grade 1 or less (except for toxicities such as alopecia or vitiligo). Note: Patients may have undergone minor surgical procedures within the past 3 weeks, as long as all toxicities have recovered to grade 1 or less or as specified in the eligibility criteria in Section 2.1.1. 14. More than four weeks must have elapsed since any prior radiation therapy. EXCLUSION CRITERIA: 1. Women of child-bearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of the preparative chemotherapy treatment on the fetus or infant. 2. Active systemic infections, coagulation disorders or other active major medical illnesses of the cardiovascular, respiratory or immune system, as evidenced by a positive stress thallium or comparable test, myocardial infarction, cardiac arrhythmias, obstructive or restrictive pulmonary disease. 3. Any form of primary immunodeficiency (such as Severe Combined Immunodeficiency Disease). 4. Concurrent opportunistic infections (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who have decreased immune competence may be less responsive to the experimental treatment and more susceptible to its toxicities). 5. Concurrent systemic steroid therapy. 6. History of severe immediate hypersensitivity reaction to any of the agents used in this study. 7. History of coronary revascularization or ischemic symptoms. 8. Any patient known to have an left ventricular ejection fraction (LVEF) less than or equal to 45%. 9. Documented LVEF of less than or equal to 45% tested in patients with i) clinically significant atrial and/or ventricular arrhythmias including but not limited to: atrial fibrillation, ventricular tachycardia, second or third degree heart block or ii) age greater than or equal 60 years old. 10. Active Bleeding