Administration of Autologous T-Cells Genetically Engineered to Express T-Cell Receptors Reactive Against Mutated or Viral Neoantigens in a Patient With Metastatic Cancer Plus the Administration of Pembrolizumab

-INCLUSION CRITERIA:

1. Measurable (per RECIST v1.1 criteria), metastatic squamous cell anal cancer.
2. Refractory to approved standard systemic therapy.
3. Clinical performance status of ECOG 0 or 1
4. Willing to practice birth control from the time of enrollment on this study and for four months after treatment.
5. Must have a negative pregnancy test because of the potentially dangerous effects of the treatment on the fetus.
6. Serology

   * Seronegative for HIV antibody. (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who are HIV seropositive may 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 RT-PCR and be HCV RNA negative.
7. Hematology

   * ANC \> 1000/mm\^3 without the support of filgrastim
   * WBC \>= 3000/mm\^3
   * Platelet count \>= 100,000/mm\^3
   * Hemoglobin \> 8.0 g/dL. Subject may be transfused to reach this cut-off.
8. Chemistry

   * Serum ALT/AST \<= 5.0 x ULN
   * Serum creatinine \<= 1.6 mg/dL
   * Total bilirubin \<= 2.0 mg/dL, except in patients with Gilbert's Syndrome, who must have a total bilirubin \< 3.0 mg/dL.
9. More than four weeks must have elapsed since completion of any prior systemic therapy at the time of enrollment. Note: Patient may have undergone minor surgical procedures or limited field radiotherapy within the four weeks prior to enrollment, as long as related major organ toxicities have recovered to grade 1 or less.
10. Ability of subject to understand and the willingness to sign a written informed consent document.
11. Willing to sign a Durable Power of Attorney Form.
12. Subject must be co-enrolled on protocol 03-C-0277.

EXCLUSION CRITERIA:

1. Patient is pregnant or breastfeeding because of the potentially dangerous effects of the treatment on the fetus or infant.
2. Concurrent systemic steroid therapy.
3. Active systemic infections requiring anti-infective treatment, coagulation disorders, or any other active or uncompensated major medical illnesses.
4. Any form of primary immunodeficiency (such as Severe Combined Immunodeficiency Disease and AIDS).
5. History of major organ autoimmune disease.
6. Grade 3 or 4 major organ irAEs following treatment with anti-PD-1/PD-L1, including but not limited to myocarditis and pneumonitis.
7. Concurrent opportunistic infections (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who have decreased immunecompetence may be less responsive to the experimental treatment and more susceptible to its toxicities.)
8. History of severe immediate hypersensitivity reaction to cyclophosphamide, fludarabine, or aldesleukin.
9. History of coronary revascularization or ischemic symptoms.
10. Patient is known to have an LVEF \<= 45%.
11. Patient is receiving any other investigational agents.