Study of Carfilzomib in Combination With Induction Chemotherapy in Children With Relapsed or Refractory Acute Lymphoblastic Leukemia

Phase 1b Key Inclusion Criteria: 1. Age 21 years or younger at the time of initial ALL diagnosis and age \> 1 year at the time of study treatment initiation. 2. Subjects must have a diagnosis of relapsed or refractory ALL with ≥ 5% blasts in the bone marrow (M2 or M3 disease), with or without extramedullary disease. -To be eligible, subjects must have had 1 or more prior therapeutic attempts, defined as: * Early first relapse (\< 36 months from original diagnosis) after achieving a CR (B-ALL) or first relapse any time following the original diagnosis after achieving a CR (T-ALL) * First refractory bone marrow relapse occurring any time after original diagnosis after achieving a CR (ie, ≥1 failed attempt to induce a second remission) OR * Relapse after achieving a CR following the first or subsequent relapse (i.e., ≥ 2 relapses) OR * Failing to achieve a CR from original diagnosis after at least 1 induction attempt 3. Subjects must have fully recovered from the acute toxic effects of all previous chemotherapy, immunotherapy, or radiotherapy treatment before enrollment. 4. Subjects must have a serum creatinine level that is ≤ 1.5 × institutional upper limit of normal (ULN) according to age. If serum creatinine level is \> 1.5 × ULN, the subject must have a calculated creatinine clearance or radioisotope glomerular filtration rate (GFR) ≥ 70 mL/min/1.73 m2. 5. Adequate liver function, defined as both of the following: * Total bilirubin ≤ 1.5 × institutional ULN except in the presence of Gilbert Syndrome * Alanine aminotransferase (ALT) ≤ 5 × institutional ULN 6. Performance status: Karnofsky or Lansky scores ≥ 50 for subjects \> 16 years old or ≤ 16 years old, respectively. Phase 2 Inclusion Criteria: 1. Subject's legally acceptable representative has provided informed consent when the subject is legally too young to provide informed consent and the subject has provided written assent based on local regulations and/or guidelines prior to any study-specific activities/procedures being initiated, except for standard of care local testing as permitted per protocol. 2. Age greater than or equal to 1 month to less than 21 years. Subjects greater than or equal to 18 years must have had their original diagnosis at less than 18 years of age. 3. Subjects must be diagnosed with relapsed or refractory relapsed ALL. 4. Subjects must have a documented first remission, less than 5% blasts in the bone marrow (M1 bone marrow) and no evidence of extramedullary disease. 5. T-cell ALL with bone marrow relapse (defined as greater than or equal to 5% leukemia blasts in bone marrow) or refractory relapse with or without extramedullary disease. OR B-cell ALL bone marrow relapse or refractory relapse (defined as greater than or equal to 5% leukemia blasts in bone marrow) after having received a targeted B-cell immune therapy (eg, blinatumomab, inotuzumab or a CAR-T therapy) with or without extramedullary disease.. 6. Adequate liver function: bilirubin less than or equal to 1.5 x upper limit of normal (ULN), alanine aminotransferase (ALT) less than or equal to 5 x ULN. 7. Adequate renal function: serum creatinine less than or equal to 1.5 x ULN or glomerular filtration rate (GFR) greater than or equal to 70 mL/min/1.73 m\^2; or for children less than 2 years of age, greater than or equal to 50 mL/min/1.73 m\^2. 8. Adequate cardiac function: shortening fraction greater than or equal to 30% or ejection fraction greater than or equal to 50%. 9. Karnofsky (subjects greater than or equal to 16 years of age) or Lansky (subjects 12 months to less than 16 years of age) performance status greater than or equal to 50%. 10. Subjects must have fully recovered from the acute toxic effects of all previous chemotherapy, immunotherapy, or radiotherapy treatment before enrollment (for example: recovery from gastrointestinal toxicity may occur more rapidly than less reversible organ toxicities such as sinusoidal obstruction syndrome or non-infectious pneumonitis, for serious prior toxicities recommended discussion with Amgen medical monitor). 11. Life expectancy of greater than 6 weeks per investigator's judgement at time of screening. Phase 1b Key Exclusion Criteria: 1. Known allergy to any of the drugs used in the study (Subjects who have had a previous allergy to PEG-asparaginase and if able, may receive Erwinia asparaginase at the investigator's discretion) 2. Known allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) 3. Left ventricular fractional shortening \< 30% 4. History of ≥ Grade 2 pancreatitis 5. Active graft-versus-host disease requiring systemic treatment 6. Positive culture for or other clinical evidence of infection with bacteria or fungus within 14 days of the initiation of study treatment 7. Down Syndrome 8. Prior therapy restrictions: * Subjects must have completed therapy with granulocyte-colony stimulating factor (G-CSF) or other myeloid growth factors at least 7 days before study treatment initiation, or at least 14 days before study treatment initiation, if pegylated myeloid growth factors were administered. * Subjects must have completed any type of active immunotherapy (e.g., tumor vaccines) at least 42 days before study treatment initiation. * Subjects must have received the last dose of a non-monoclonal antibody biologic agent at least 7 days before study treatment initiation. * At least 3 antibody half-lives must have elapsed since the last dose of monoclonal antibody (e.g., 66 days for rituximab and 69 days for epratuzumab) before subjects may initiate study treatment. * Subjects must not have received other antineoplastic agents with therapeutic intent, excluding hydroxyurea and antimetabolites administered as part of maintenance chemotherapy, within 7 days prior to study treatment initiation. 9. Hepatitis B infection with positive hepatitis B DNA Phase 2 Exclusion Criteria: 1. Prior treatment with carfilzomib. 2. Intolerance, hypersensitivity, or inability to receive any of the chemotherapy components of the VXLD regimen. An exception is allowed for allergy to asparaginase products if Erwinia asparaginase is unable to be administered, 3. Autologous HSCT within 6 weeks prior to start of study treatment. 4. Allogeneic HSCT within 3 months prior to start of study treatment. 5. Active GVHD requiring systemic immune suppression. 6. Less than 30 days from discontinuation of immune suppressive therapy administered for the treatment of acute or chronic GVHD. 7. Isolated extramedullary relapse. 8. Positive bacterial or fungal infection within 14 days of enrollment (except for documented line infection, line has been removed, and blood culture after line removal is negative for 5 days prior to first dose of induction therapy). Antibiotics may be administered for prophylaxis as per institutional standards up to and after enrollment. 9. Subjects with less than 3 antibody half-lives since the last dose of monoclonal antibody (eg, 66 days for rituximab, 69 days for epratuzumab, inotuzumab for 36 days), prior to first dose of investigational product must be discussed with the Amgen medical monitor and may be allowed to enroll based on extent of disease or evidence of rapidly rising peripheral or bone marrow blast counts. 10. Cell-based immunotherapy (eg, donor leucocyte infusion, CAR-T cells, tumor vaccines) within 42 days prior to first dose of investigational product. If the Amgen medical monitor agrees, an exception may be granted to the 42-day requirement for subjects with rapidly rising peripheral or bone marrow blast counts. 11. Down's syndrome. 12. Presence of another active cancer. 13. History of grade greater than or equal to 2 pancreatitis within 6 months to screening. 14. Unresolved toxicities from prior anticancer therapy, defined as not having resolved to CTCAE version 4.03 grade 1 or to levels dictated in the eligibility criteria apart from alopecia or toxicities from prior anticancer therapy that are considered irreversible and do not trigger another exclusion criterion (defined as having been present and stable for greater than 4 weeks). 15. Antitumor therapy (chemotherapy, investigational agents, molecular-targeted therapy) within 7 days of day 1 of induction. Exception: hydroxyurea to control peripheral blood leukemic cell counts is allowed until start of investigational product. 16. Active viral infection, including but not limited to cytomegalovirus (CMV), Hepatitis B infection with positive serum hepatitis surface antigen or hepatitis B DNA, HIV, Hepatitis C with detectable hepatitis C RNA. Subjects who have previously received a stem cell transplant must be screened for CMV infection, unless both subject and donor are known to be CMV negative. 17. Currently receiving treatment in another investigational device or product study, or less than 14 days since ending treatment on another investigational device or product study. 18. Uncontrolled arrhythmias or screening ECG with corrected QT interval (QTc) of greater than 470 msec. 19. History or evidence of any other clinically significant disorder, condition or disease (with the exception of those outlined above) that, in the opinion of the investigator or Amgen physician, if consulted, would pose a risk to subject safety or interfere with the study evaluation, procedures or completion. 20. Female subject is pregnant or breastfeeding or planning to become pregnant or breastfeed during treatment and for an additional 6 months after the last dose of any study treatment or for 12 months after last dose of cyclophosphamide if administered during optional consolidation cycle. 21. Female subjects of childbearing potential unwilling to use 1 highly effective method of contraception during treatment and for an additional 6 months after the last dose of any study treatment or for 12 months after last dose of cyclophosphamide if administered during optional consolidation cycle. 22. Female subjects of childbearing potential with a positive pregnancy test assessed at Screening by a serum or urine pregnancy test. 23. Male subjects with a female partner of childbearing potential who are unwilling to practice sexual abstinence (refrain from heterosexual intercourse) or use a condom with spermicide during treatment and for an additional 6 months after the last dose of any study treatment, even if they have undergone a successful vasectomy. 24. Male subjects with a pregnant partner who are unwilling to practice abstinence or use a condom with spermicide during treatment, for duration of pregnancy, and for an additional 6 months after the last dose of any study treatment. 25. Male subjects unwilling to abstain from donating semen or sperm during treatment and for an additional 6 months after the last dose of any study treatment. 26. Known allergy to captisol (a cyclodextrin derivative used to solubilize carfilzomib; for a complete listing of Captisol-enabled drugs, see the Ligand Pharmaceuticals, Inc. website).