Inclusion Criteria:

          -  Patients with a diagnosis of relapsed or refractory leukemia including, but not
             limited to acute myeloid leukemia (AML), acute lymphoblastic leukemia (ALL), T-cell
             prolymphocytic leukemia, biphenotypic acute leukemia, or blast-phase of chronic
             myeloid Leukemia (CML) will be allowed during the safety lead-in phase

          -  For cohort A of the expansion phase: Patients with a diagnosis untreated adverse-risk
             AML (as defined by ELN [European Leukemia Net Classification] 2017) will be enrolled

          -  For cohort B of the expansion phase: Patients with a diagnosis of relapsed or
             refractory AML will be enrolled

          -  Bilirubin =< 2 mg/dL

          -  Aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) =< 2.5 x upper
             limit of normal (ULN)

          -  Creatinine =< 1.5 x ULN

          -  Cardiac ejection fraction of > or = 45% within the past 3 months

          -  Amylase and lipase =< 1.5 x ULN

          -  Eastern Cooperative Oncology Group (ECOG) performance status of =< 2

          -  A negative urine pregnancy test is required within one week (7 days) for all women of
             childbearing potential prior to being registered on this trial

          -  Patient must have the ability to understand the requirements of the study and signed
             informed consent. A signed informed consent by the patient or his legally authorized
             representative is required prior to their enrollment on the protocol

        Exclusion Criteria:

          -  Pregnant women are excluded from this study because the agents used in this study have
             the potential for teratogenic or abortifacient effects. Because there is a potential
             risk for adverse events in nursing infants secondary to treatment of the mother with
             the chemotherapy agents, breastfeeding should also be avoided

          -  Uncontrolled intercurrent illness including, but not limited to active uncontrolled
             infection, symptomatic congestive heart failure (New York Heart Association [NYHA]
             class III or IV), unstable angina pectoris, clinically significant cardiac arrhythmia,
             or psychiatric illness/social situations that would limit compliance with study
             requirements

          -  Patient with documented hypersensitivity to any of the components of the chemotherapy
             program

          -  Prior treatment with pegylated asparaginase

          -  Patients with a diagnoses of acute promyelocytic leukemia (AML-M3) will be excluded
             from this trial

          -  Men and women of childbearing potential who do not practice contraception. Women of
             childbearing potential and men must agree to use contraception prior to study entry
             and for the duration of study participation. Effective methods of birth control
             include:

               -  Birth control pills, shots, implants or patches

               -  Intrauterine devices (IUDs)

               -  Condom or occlusive cap (diaphragm or cervical/vault caps) used with spermicide

               -  Abstinence

               -  Females of non-childbearing potential are those who are postmenopausal greater
                  than 1 year or who have had a bilateral tubal ligation, oophorectomy, and/or
                  hysterectomy

          -  Patients with history of clinically significant venous thromboembolism