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 BLOOD MONONUCLEAR CELL (PBMC) COLLECTION * Research participant must not require more than 2 mg three times daily (TID) of dexamethasone on the day of PBMC collection. * Research participant must have appropriate venous access * At least 2 weeks must have elapsed since the research participant received his/her last dose of prior targeted agents, chemotherapy or radiation; at the principal investigator's discretion, exception can be made for investigational agents that are delivered locally into the CSF * ELIGIBILITY TO PROCEED WITH RICKHAM PLACEMENT * Once research participants meet eligibility to proceed with Rickham placement, they will be deemed accrued on to the study * Note: if the participant had received prior targeted radiation and new lesions have appeared outside of that targeted area, then that may be deemed radiographic evidence of measurable disease even if 12 weeks have not elapsed * Creatinine \< 1.6 mg/dL * White blood cell (WBC) \> 2,000/dl (or absolute neutrophil count \[ANC\] \> 1,000) * Platelets \>= 100,000/dl * International normalized ratio (INR) \< 1.3 * Bilirubin \< 1.5 mg/dL * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \< 2.5 x upper limits of normal * ELIGIBILITY TO PROCEED WITH CAR T CELL INFUSION * Research participant has a released cryopreserved CAR T cell product * Research participant does not require supplemental oxygen to keep saturation greater than 95% and/or does not have presence of any radiographic abnormalities on chest x-ray that are progressive * Research participants does NOT have any known history of congestive heart failure (CHF) or cardiac symptoms consistent with NYHA classification III-IV within 6 months prior to Day 1 of protocol treatment, cardiomyopathy, myocarditis, myocardial infarction (MI), exposure to cardiotoxic medications or with clinical history suggestive of the above must have an EKG and echocardiogram (ECHO) performed within 42 days prior to registration and as clinical indicated while on treatment * If the research participant has new symptoms of CHF, cardiomyopathy, myocarditis, MI, or exposure to cardiotoxic medications they already had a cardiac consultation, creatinine phosphokinase (CPK), and troponin testing at pre study deeming them fit for study participation * Research participant does not have a fever exceeding 38.5 degrees Celsius (C); there is an absence of positive blood cultures for bacteria, fungus, or virus within 48-hours prior to T cell infusion and/or there aren't any indications of meningitis * Research participant serum total bilirubin or transaminases does not exceed 2 x normal limit * Research participant serum creatinine \< 1.8 mg/dL * Research participant does not have uncontrolled seizure activity following surgery prior to starting the first T cell dose * Research participant platelet count must be \> 100,000; however, if platelet level is between 75,000-99,000, then CAR T-cell infusion may proceed after platelet transfusion is given and the post transfusion platelet count is \>= 100,000 * Research participants must not require more than 2 mg TID of dexamethasone during CAR T cell therapy * Wash-out requirements (standard or investigational): * At least 6 weeks since the completion of a nitrosourea-containing chemotherapy regimen; and * At least 23 days must have passed since the completion of Temodar and/or 4 weeks for any other non-nitrosourea-containing cytotoxic chemotherapy regimen; if a participant's most recent treatment was with a targeted agent only, and s/he has recovered from any toxicity of this targeted agent, then a waiting period of only 2 weeks is needed from the last dose and the start of CAR T cell infusion with the exception of bevacizumab where a wash out period of at least 4 weeks is required before starting CAR T cell therapy Exclusion Criteria: * Research participant requires supplemental oxygen to keep saturation greater than 95% and the situation is not expected to resolve within 2 weeks * Research participants with a known history of congestive heart failure (CHF) or cardiac symptoms consistent with New York Heart Association (NYHA) classification III-IV within 6 months prior to Day 1 of protocol treatment, cardiomyopathy, myocarditis, myocardial infarction (MI), exposure to cardiotoxic medications or with clinical history suggestive of the above must have an electrocardiogram (EKG) and echocardiogram (ECHO) performed within 42 days prior to registration and as clinically indicated while on treatment * Research participants with new symptoms of CHF, cardiomyopathy, myocarditis, MI, or exposure to cardiotoxic medications must have a cardiac consultation, creatinine phosphokinase (CPK), and troponin testing at pre -study and as clinically indicated * Research participant requires dialysis * Research participant has uncontrolled seizure activity and/or clinically evident progressive encephalopathy * Failure of research participant to understand the basic elements of the protocol and/or the risks/benefits of participating in this phase I study; a legal guardian may substitute for the research participant * Research participants with any non-malignant intercurrent illness which is either poorly controlled with currently available treatment, or which is of such severity that the investigators deem it unwise to enter the research participant on protocol shall be ineligible * Research participants with any other active malignancies * Research participants being treated for severe infection or who are recovering from major surgery are ineligible until recovery is deemed complete by the investigator * Research participants with any uncontrolled illness including ongoing or active infection; research participants with known active hepatitis B or C infection; research participants with any signs or symptoms of active infection, positive blood cultures or radiological evidence of infections * Research participants who have confirmed human immunodeficiency virus (HIV) positivity within 4 weeks of enrollment