Anti-EGFRvIII synNotch Receptor Induced Anti-EphA2/IL-13Ralpha2 CAR (E-SYNC) T Cells

This phase I trial tests the safety, side effects, and best dose of E-SYNC chimeric antigen receptor (CAR) T cells after lymphodepleting chemotherapy in treating patients with EGFRvIII positive (+) glioblastoma. Chimeric antigen receptor (CAR) T-cell therapy is a type of treatment in which a patient's T cells (a type of immune system cell) are changed in the laboratory so the CAR T cells will attack cancer cells. T cells are taken from a patient's blood. Then the gene for a special receptor that binds to a certain protein on the patient's cancer cells is added to the T cells in the laboratory. The special receptor is called a chimeric antigen receptor. Large numbers of the CAR T cells are grown in the laboratory and given to the patient by infusion for treatment of certain cancers. Lymphodepleting chemotherapy with cyclophosphamide and fludarabine before treatment with CAR T cells may make the CAR T cells more effective.

Inclusion Criteria: * Inclusion Criteria for Cohort 1: 1. Age \>= 18 years. 2. Karnofsky performance status (KPS) score of \>=70. 3. All participants must have adequate organ function defined as: 1. Peripheral absolute neutrophil count \>=1000/mm\^3. 2. Platelet count \>=100,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment). 3. Absolute lymphocyte count (ALC) \>= 300/μL and/or Cluster of differentiation 3 (CD3) count of \>=150/μL. 4. Creatinine clearance or radioisotope glomerular filtration rate \>= 50 mL/min/1.73m\^2. 5. Total Bilirubin \