Feasibility of Using Bortezomib With or Without Chemotherapy in Patients With Atypical Teratoid/Rhabdoid Tumors

Inclusion Criteria: 1. Patients with a valid Informed Consent Form signed by the Legal Guardian and/or Patient himself/herself. 2. Patients with CNS AT/RT who were initially diagnosed at the age of 0-20 years. 3. Disease Status: Cohort 1: Patients with newly diagnosed AT/RT; Cohort 2: Patients with recurrent or refractory CNS AT/RT who have had at least 1 line of chemotherapy with radiographically measurable disease as defined by at least 1 lesion that can be measured in 2 dimensions. 4. Previous Anticancer Therapy: Cohort 1: No previous anticancer chemotherapy other than the use of corticosteroids. Cohort 2: Patient has fully recovered from the acute toxic effects of chemotherapy, immunotherapy, or radiation therapy prior to entering this study: * Myelosuppressive chemotherapy: Patient has not received myelosuppressive chemotherapy within 3 weeks of enrollment onto this study (4 and 6 weeks if prior temozolomide and nitrosourea, respectively). * Hematopoietic growth factors: At least 7 days must have elapsed since the completion of therapy with a growth factor. At least 14 days must have elapsed after receiving pegfilgrastim. * Biologic (anti-neoplastic agent): At least 7 days must have elapsed since completion of therapy with a biologic agent. For agents that have known adverse events occurring beyond 7 days after administration, this period prior to enrollment must be extended beyond the time during which adverse events are known to occur. * Monoclonal antibodies: At least 3 half-lives must have elapsed since prior therapy that included a monoclonal antibody. * Radiation therapy: at least 3 months must have elapsed since any irradiation unless measurable disease progression occurs at a site separate from the irradiated area and the patient has recovered from toxicities associated with radiation therapy. 5. Patients must have adequate organ and marrow function as defined below at enrollment and on day 1 of (or within 1 week prior to) each cycle: * Absolute Neutrophil Count (ANC) ≥ 1,000/μL * Platelets ≥ 100,000/μL at enrollment and on day 1 of each cycle * Hemoglobin ≥ 8 g/dL (RBC transfusions allowed) * Total bilirubin ≤ 1.5 times institutional upper limit of normal * AST (SGOT) and ALT (SGPT) ≤ 2.5 times institutional upper limit of normal (4x ULN if liver involvement) * Creatinine ≤ upper limits by age 0-5 years old: 0.8 mg/dL; 6-9 years old: 1.0 mg/dL; 10-12 years old: 1.2 mg/dL; 13-15 years old: male, 1.5 mg/dL; female, 1.4 mg/dL; 16 years or older: male, 1.7 mg/dL; female, 1.4 mg/dL 6. LV Ejection Fraction of ≥ 50% by Echocardiogram 7. Patient must have the Performance status defined by Lansky (\< 16 years of age) or Karnofsky (≥16 years of age) Performace Status of ≥ 30 (Cohort 1) or ≥ 60 (Cohort 2). 8. Patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered to be ambulatory for the purpose of assessing the performance score. 9. Female patients who are at least 10-years-old or are post-menarchal must have a negative serum or urine pregnancy test prior to enrollment 10. Fertile patients must use effective contraception 11. Life expectancy \> 8 weeks 12. No evidence of dyspnea at rest 13. Fertile patients must use effective contraception Exclusion Criteria: 1. Clinically significant medical disorders that could compromise the ability to tolerate protocol therapy or that would interfere with the study procedures or results history. 2. Presence of an active, uncontrolled infection. 3. Existing peripheral neuropathy of NCI CTCAE v5.0 grade 2 or higher. 4. Patients who have not recovered to baseline from previous treatment. 5. Patients with hypersensitivity (not including local reactions) to BTZ, boron, or mannitol. 6. Patients who have been previously treated with BTZ. 7. Requirement for constant administration of strong CYP3A4 interfering agents. 8. Treatment with clinically significant enzyme inducers, such as the enzyme-inducing antiepileptic drugs phenytoin, carbamazepine or phenobarbital, or with rifampin, rifabutin, rifapentine, or St. John's wort within 7 days prior to initiation of BTZ. 9. Inability to comply with the safety monitoring requirements of the study, as judged by the investigator. 10. Female participants of childbearing potential cannot be pregnant or breast-feeding. 11. Patients who are receiving other investigational drugs 14 or fewer days before enrollment. 12. Patients with extra-CNS, extrarenal rhabdoid tumors or malignant renal rhabdoid tumors without CNS AT/RT are not eligible. 13. Myocardial infarction within 6 months prior to enrollment or New York Heart Association Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. If for some reason an electrocardiogram is obtained before study enrollment, any abnormalities detected should be documented as clinically irrelevant. 14. Other severe acute or chronic medical or psychiatric condition or any laboratory abnormality that may increase the risk associated with study participation or investigational product administration or that may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for enrollment in this study. 15. Subjects with known active infections requiring ongoing treatment (bacterial, fungal, or viral, including human immunodeficiency virus \[HIV\]).