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

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 \<= 1.5 x ULN except for Gilbert's syndrome and 6. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \<= 3x upper limit of normal (ULN). 7. Left ventricular ejection fraction (LVEF) \>= 50% by echocardiogram or multi-gated acquisition scanning (MUGA). 8. Adequate pulmonary function, defined as no evidence of dyspnea at rest and pulse oximetry \> 92% while breathing room air. 4. Pathological criteria: EGFRvIII+ GBM from most recent surgery, confirmed by a Clinical Laboratory Improvement Amendments (CLIA)-certified lab using a next-generation sequencing panel. 5. MGMT promoter must be unmethylated or with a methylation index \< 3. 6. Must have completed at least standard of care (SOC) external beam radiotherapy (EBRT) as initial therapy. 7. Participants must be anticipated to be able to complete E-SYNC T cell infusion within 12 weeks after completion of EBRT. 8. All participants must be off systemic steroids for 3 days or more prior to leukapheresis. 9. Must be willing to provide voluntary informed consent for apheresis (and tissue screening if needed) and for study treatment. NOTE: There are two sets of eligibility criteria for Cohort 2. Tissue Screening: Defines eligibility for tissue screening and to determine H-score. Study Enrollment: Defines eligibility for study enrollment and E-SYNC T cell manufacturing/treatment. * Inclusion Criteria for Tissue Screening Cohort 2: 1. Age \>=18 years. 2. Pathological criteria: EGFRvIII+ GBM from most recent surgery, confirmed by a Clinical Laboratory Improvement Amendments (CLIA)-certified lab using a next-generation sequencing panel. * Inclusion Criteria for Study Enrollment for Cohort 2 1. Karnofsky Performance Scale (KPS) score \>=70. 2. received at least standard of care external beam radiotherapy (SOC EBRT) as initial therapy, with or without concurrent temozolomide (TMZ), and completed the last dose of TMZ ≥23 days prior to study enrollment). Note: patients may have initiated adjuvant TMZ +/- TTFields. 3. Pathological criteria: EGFRvIII+ GBM from most recent surgery, as defined by an EGFRvIII H-score of ≥ 150 based on central review. 4. Is surgically amenable, with expectation for ability to resect at least 500 mg of tumor tissue confirmed by participant's neurosurgeon. 5. Participants with reproductive potential agree to use reliable and double barrier method of contraception during the study and for at least 6 months after the last study intervention, including refraining from donating sperm during this period. 6. Females of childbearing potential must have a negative serum beta-human chorionic gonadotropin (HCG) pregnancy test prior to receiving study interventions. 7. All participants must have adequate organ function. a. Adequate bone marrow function is defined as: i. Peripheral absolute neutrophil account ≥ 1000/mm3 and ii. Platelet count ≥ 100,000/mm3 (transfusion dependent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) and iii. Absolute lymphocyte count (ALC) ≥ 300/µL and/or CD3 count of ≥ 150/µL b. Adequate renal function is defined as: i. Creatinine clearance or radioisotope glomerular filtration rate ≥ 50 mL/min/1.73m2 c. Adequate liver function is defined as: i. Total Bilirubin ≤ 1.5 x upper limit of normal (ULN) except for Gilbert's syndrome and ii. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3 x ULN d. Coagulation tests prothrombin time (PT) and partial thromboplastin time (PTT) have to be within normal limits, unless the participant has been therapeutically anti-coagulated for previous venous thrombosis. e. Adequate pulmonary function, defined as no evidence of dyspnea at rest and pulse oximetry \> 92% while breathing room air. f. Adequate cardiac function, confirmed within the last 12 months, defined as: i. Left ventricular ejection fraction (LVEF) ≥ 40% by echocardiogram or multi-gated acquisition scanning (MUGA) 8. Must be willing to provide voluntary informed consent for study intervention. Exclusion Criteria: * Exclusion Criteria for Cohort 1 1. Participant who has been treated with any investigational agents and chemotherapy targeting GBM \<= 4 weeks prior to date of study registration. Exceptions to this include: must be \>=23 days from last dose of temozolomide (TMZ) or radiotherapy, mush be \>= 6 weeks from last dose of nitrosourea. 2. Female participants of reproductive potential who are pregnant or lactating. Female study participants of reproductive potential must have a negative serum pregnancy test as part of eligibility confirmation. 3. Known addiction to alcohol or illicit drugs. 4. Prior treatment with any Epithelial Growth Factor Receptor (EGFR)-targeting therapy. 5. Participants with leptomeningeal dissemination. 6. Participants with a known disorder that affects their immune system, such as human immunodeficiency virus (HIV) or an autoimmune disorder requiring systemic cytotoxic or immunosuppressive therapy. Participants who are currently using non-systemic steroids (e.g., inhaled, intranasal, ocular, topical) are not excluded from the study. 7. Participants with serologic status reflecting active hepatitis B or C infection. Participants that are positive for hepatitis B surface antigen (HBsAg+) will be