Memory-Enriched T Cells in Treating Patients With Recurrent or Refractory Grade III-IV Glioma

Inclusion Criteria: * Participant has a prior histologically-confirmed diagnosis of a grade III or IV glioma, or has a prior histologically-confirmed diagnosis of a grade II glioma and now has radiographic progression consistent with a grade III or IV malignant glioma (MG) * Karnofsky performance status (KPS) \>= 60% * Life expectancy \> 4 weeks * The effects of HER2(EQBBzeta/CD19t+ T cells on the developing fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately * City of Hope (COH) Clinical Pathology confirms HER2+ tumor expression by immunohistochemistry (\>= 20%, 1+) * All research participants must have the ability to understand and the willingness to sign a written informed consent * Note: For research participants who do not speak English, a short form consent may be used with a COH certified interpreter/translator to proceed with screening and leukapheresis, while the request for a translated full consent is processed; however, the research participant is allowed to proceed with rickham placement and CAR T cell infusion only after the translated full consent form is signed * ELIGIBILITY TO PROCEED WITH PERIPHERAL BL…