Intracranial Genetically Modified Immune Cells (TGFβR2KO/IL13Rα2 CAR T-Cells) for the Treatment of Recurrent or Progressive Glioblastoma or Grade 3 or 4 IDH-Mutant Astrocytoma

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Note: For research participants who do not speak English, a short form consent may be used with a City of Hope (COH) certified interpreter/translator to proceed with screening and leukapheresis, while the request for a translated main consent is processed. However, the research participant is allowed to proceed with surgery/Rickham placement and CAR T cell infusion only after the translated main consent form is signed * Agreement to allow the use of archival tissue from diagnostic tumor biopsies. If unavailable, exceptions may be granted with study principal investigator (PI) approval * Age: ≥ 18 years * Karnofsky performance status (KPS) ≥ 70%, Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Life expectancy ≥ 4 weeks * If the participant has a shunt, they must be informed of the following: * If the shunt is not programmable, the participant must be willing to have a programmable shunt placed prior to CAR T cell infusion, and * If the shunt is programmable, in order to proceed to the treatment portion of the study, the participant must be able to tolerate their shunt being functionally closed for at least 2 hours * Participant has a prior histologically-confirmed diagnosis of a grade 3 or 4 IDH-mutant astrocytoma or glioblastoma, or has a prior histologically-confirmed diagnosis of a grade 2 or 3 astrocytoma and now has radiographic progression consistent with grade 3 or 4 IDH-mutant astrocytoma * Relapsed disease: radiographic evidence of recurrence/progression of measurable disease after standard therapy, and ≥ 12 weeks after completion of front-line radiation therapy * COH clinical pathology confirms IL13Rα2+ tumor expression by immunohistochemistry (H-score ≥ 80) * No known contraindications to leukapheresis, steroids, or tocilizumab * White blood cell (WBC) \> 2000 /dl (or absolute neutrophil count \[ANC\] ≥ 1,000/mm\^3) (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Platelets ≥ 75,000/mm\^3 (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Hemoglobin ≥ 8g/dl (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Aspartate aminotransferase (AST) ≤ 2.5 x ULN (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Alanine aminotransferase (ALT) ≤ 2.5 x ULN (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Serum creatinine ≤ 1.6 mg/dL (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Oxygen (O2) saturation ≥ 95% on room air (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Seronegative for HIV antigen/antibody (Ag/Ab) combo, hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative) (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Women of childbearing potential (WOCBP): Negative urine or serum pregnancy test (to be performed within 14 days prior to leukapheresis unless otherwise stated) * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 3 months after the last dose of protocol therapy * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Owing to higher frequency of wound-related complications, participants who require active bevacizumab therapy at the time of enrollment are excluded * Participant has not yet recovered from toxicities of prior therapy * Uncontrolled seizure activity and/or clinically evident progressive encephalopathy * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent * Clinically significant uncontrolled illness * Active autoimmune disease requiring systemic immunosuppressive therapy * Active infection requiring intravenous (IV) antibiotics (e.g., minor scalp infection is not an exclusion) * Known history of human immunodeficiency virus (HIV) or hepatitis B or hepatitis C infection * Other active malignancy. Note: Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Females only: Pregnant or breastfeeding * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)