Inclusion Criteria:
1. Participants must have histologically and molecularly confirmed newly diagnosed World Health Organization (WHO) grade 3 or 4 glioma.
1. Phase 1: any newly diagnosed HGG (including DMG of any location and primary spinal cord tumors).
2. Phase 2:
* Cohort 1: Newly diagnosed non-pontine, non-spinal cord HGG histone-wildtype.
* Cohort 2: Newly diagnosed non-pontine, non-spinal cord H3K27 altered diffuse midline glioma (DMG).
* Cohort 3: Newly diagnosed non-pontine, non-spinal cord H3G34 mutant diffuse hemispheric glioma (DHG).
2. Prior surgery: must have undergone maximal safe resection. For patients with DMG of the pons, biopsy is sufficient.
3. Prior Therapy: Participants must NOT have received ANY prior therapy (except surgery) before enrollment on study.
4. Tumor Tissue Requirement: Participants must have sufficient tumor tissue (5-10 unstained formalin-fixed paraffin-embedded (FFPE) slides or a tumor block) for study enrollment.
5. Age:
Phase 1:
o 3 to \<18 years of age.
Phase 2:
* Cohort 1: 3 to 25 years of age.
* Cohorts 2 \& 3: 3 to 39 years of age.
6. Performance Score: Karnofsky \>= 50 for participants \> 16 years of age and Lansky \>= 50 for participants \<=16 years of age. Participants who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score.
7. Corticosteroids: Participants who are receiving dexamethasone must be on a stable or decreasing dose for at least 1 week prior to registration.
8. Organ Function Requirements:
1. Peripheral absolute neutrophil count (ANC) \>= 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. Creatinine Clearance (CrCl) or estimated glomerular filtration rate (eGFR) with cutoff value of ≥ 60 mL/min for renal function in participants with age ≥ 18 years. For participants \< 18 years old, estimate eGFR using the Schwartz equation. eGFR (mL/min/1.73 m\^2) = (k × Height (cm)) / Serum Creatinine (mg/dL).
4. Total bilirubin \<= 1.5 x upper limit of normal (ULN) for age; in presence of Gilbert's syndrome, total bilirubin \< 3 x ULN or direct bilirubin \< 1.5 x ULN.
5. alanine aminotransferase (ALT) \<= 3 x ULN.
6. aspartate aminotransferase (AST) \<= 3 x ULN.
7. Participants with seizure disorder may be enrolled if well controlled. Participants on non-enzyme inducing anticonvulsants may be excluded pending interaction(s) with study drug.
9. The effects of ADI-PEG 20 have been shown to be associated with embryofetal toxicity in rodents. For this reason and because chemotherapy used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation and 4 months after completion of treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.
10. A legal parent/guardian or participant must be able to understand, and willing to sign, a written informed consent and assent document, as appropriate.
11. Participants must enroll on PNOC COMP if PNOC COMP is open to accrual at the enrolling institution.
Exclusion Criteria:
1. Participants who have received any systemic therapy or RT, including any investigational agents.
2. History of allergic reactions attributed to compounds of similar chemical or biologic composition to ADI-PEG 20 such as pegylated compounds.
3. Phase 2 cohorts: tumors with epicenter in pons or spinal cord
4. Participants with metastatic or leptomeningeal disease. Multi-focal disease should be discussed with the study chairs,
5. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection that would interfere with the study.
6. Women of childbearing potential must not be pregnant or breast-feeding.
7. Human immunodeficiency virus (HIV)-positive participants will be ineligible if HIV therapy regimen has not been stable for at least 4 weeks or there is intent to change the regimen within 8 weeks following enrollment, or if they are severely immunocompromised.
8. Corrected QT Interval (QTc) cutoff \>480 ms.
Important note: The eligibility criteria listed above are interpreted literally and cannot be waived.
