Genetically Engineered Cells (B7-H3-Specific CAR T Cells) in Treating Pediatric Patients with Diffuse Intrinsic Pontine Glioma, Diffuse Midline Glioma, or Recurrent or Refractory Central Nervous System Tumors

Inclusion Criteria

• Subjects must be age >= 1 and =< 26 years (except for the first 3 subjects, who will be enrolled in Arm A or Arm B and must be age >= 15 and =< 26 years) (this requirement has been met as of 8/27/2020).
• Subject disease classified as one of the following: * DIPG at any timepoint following completion of standard radiotherapy * DMG at any timepoint following completion of standard radiotherapy * Evidence of refractory or recurrent CNS disease for which there is no standard therapy, defined by either of the following: ** Recurrent disease (e.g., new site[s] of measurable or evaluable disease by radiographic imaging or histologic confirmation following completion of standard of care first-line therapy for which curative salvage therapy is not available or amenable, OR ** Refractory disease (e.g., measurable or evaluable disease that persists following completion of standard of care first-line therapy for which curative salvage therapy is not available or amendable)
• Able to tolerate apheresis or already has an apheresis product available for use in manufacturing.
• CNS reservoir catheter, such as an Ommaya or Rickham catheter, present in the proper location for CNS-directed therapy delivered as specified for BrainChild-03.
• Life expectancy >= 8 weeks.
• Lansky or Karnofsky score >= 60. Subjects who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for purposes of assessing performance status.
• If subject does not have a previously obtained apheresis product that is acceptable and available for manufacturing of CAR T cells, subject must discontinue all anti-cancer agents and radiotherapy and, in the opinion of the investigator, have fully recovered from significant acute toxic effects of the following: * Cytotoxic chemotherapy/biologic therapy: All cytotoxic chemotherapy/biologic therapy must be discontinued >= 7 days prior to enrollment. * Antibody therapy: The last dose of anti-tumor antibody therapy (including check point inhibitor) must be at least 3 half-lives or 30 days, whichever is shorter, from the time of enrollment. Bevacizumab will be considered biologic therapy. * Cellular therapy: must be at least 30 days from most recent cell infusion prior to enrollment * Steroid use: All systemically administered (i.e. subcutaneous, intramuscular, orally [PO] or intravenously [IV]) corticosteroid therapy (unless physiologic replacement dosing) must be stable or decreasing for >= 1 week prior to enrollment, with a maximum dexamethasone dose of 2.5 mg/m^2/day ongoing at enrollment. Corticosteroid physiologic replacement therapy for management of pituitary/adrenal axis insufficiency and/or topical administration (e.g. inhaled or dermatologic) is allowed.
• Absolute lymphocyte count (ALC) >= 100 cells/uL. * Value not required to be met if subject has previously obtained apheresis product acceptable and available for manufacturing of CAR T cells
• Absolute neutrophil count (ANC) >= 500 cells/uL.
• Hemoglobin >= 9 g/dL. * Subjects receiving blood product transfusion(s) are acceptable as long as they are not determined to be transfusion refractory.
• Platelets >= 100,000/uL. * Subjects receiving blood product transfusion(s) are acceptable as long as they are not determined to be transfusion refractory.
• Serum creatinine =< the upper limit of normal (ULN) based on age and sex. * Maximum serum creatinine (mg/dL): ** Age 1 to < 2 years (yrs): 0.6 mg/dL (male); 0.6 mg/dL (female) ** Age 2 to < 6 yrs: 0.8 mg/dL (male); 0.8 mg/dL (female) ** Age 6 to < 10 yrs: 1 mg/dL (male); 1 mg/dL (female) ** Age 10 to < 13 yrs: 1.2 mg/dL (male); 1.2 mg/dL (female) ** Age 13 to < 16 yrs: 1.5 mg/dL (male); 1.4 mg/dL (female) ** Age >= 16 yrs: 1.7 mg/dL (male); 1.4 mg/dL (female)
• Total bilirubin < 3 times ULN for age OR conjugated bilirubin < 2 mg/dL.
• Oxygen saturation >= 90% on room air without supplemental oxygen or mechanical ventilation, AND no dyspnea at rest.
• Signs and symptoms of neurologic deficit must be stable for >= 1 week prior to enrollment, AND =< two anti-epileptic agents are required to control seizure activity, AND no clinically evident encephalopathy present.
• Virology negative within 3 months prior to enrollment, to include all of the following: * Human immunodeficiency virus (HIV) antigen & antibody, AND * Hepatitis B surface antigen, AND * Hepatitis C antibody OR if antibody positive, hepatitis C polymerase chain reaction (PCR) is negative.
• Subjects of childbearing/fathering potential must agree to use highly effective contraception from the time of enrollment through 12 months following the last T cell infusion.

Exclusion Criteria

• Presence of >= grade 3 cardiac dysfunction or symptomatic arrhythmia requiring intervention.
• Presence of primary immunodeficiency/bone marrow failure syndrome.
• Presence of clinical and/or radiographic evidence of impending herniation.
• For Arm C subjects only: Presence of > grade 3 dysphagia.
• Presence of active malignancy other than the CNS tumor under study.
• Presence of active severe infection, defined as either of the following * Positive blood culture within 48 hours of enrollment, OR * Fever >= 38.2 degrees Celsius AND clinical signs of infection within 48 hours of enrollment.
• Pregnant or breastfeeding.
• Subject and/or authorized legal representative unwilling to provide consent/assent for study participation, including participation in the 15-year follow-up period, which is required if CAR T cell therapy is administered.
• Presence of any condition that, in the opinion of the investigator, would prohibit the subject from undergoing treatment under this protocol.