Inclusion Criteria:

• World Health Organization (WHO)-defined acute lymphoblastic leukemia and either:
  • Relapsed after achieving remission
  • Refractory to front line therapy
  • Newly diagnosed and ineligible for intensive chemotherapy induction Note: patients with T lineage and B lineage ALL are eligible for this trial; likewise, patients with Philadelphia chromosome positive (Ph+) (as long as they are not candidate for other therapies for Ph+) and Ph- ALL are eligible
• Bone marrow blasts of at least 10%
• At least 4 weeks away from any previous antineoplastic or investigational agent; patients may receive hydroxyurea or glucocorticoids for suppression of leukocytosis, but these must be stopped at least 24 hours prior to initiation of therapy
• Eastern Cooperative Oncology Group (ECOG) performance status =< 2
• Life expectancy of > 2 months
• Total bilirubin =< 1.5 × institutional upper limit of normal
• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 × institutional upper limit of normal
• Creatinine =< 1.5 × institutional upper limit of normal
• Fasting blood glucose (FBG) < 130 mg/dL
• HbA1C < 7.0%
• Relapse after SCT is allowed but no active graft-versus-host disease (GVHD) as per treating physician; also must not exceed the number of prior induction regimens listed above; SCT does not count as line of therapy
• Women of child-bearing potential and men must agree to use 1 highly effective method of contraception and 1 additional effective (barrier) method, at the same time, from the time of signing the informed consent through 90 days (or longer, as mandated by local labeling [e.g. United States product insert (USPI), Summary of Product Characteristics (SmPC), etc]) after the last does of study drug; 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; men treated or enrolled on this protocol must also agree to use highly effective barrier contraception prior to the study, for the duration of study participation, and 4 months after completion of MLN0128 (TAK-228) administration
• Ability to understand and the willingness to sign a written informed consent document
• No prior therapy with mTOR inhibitors except for rapalog treatment as part of graft-versus-host (GVH) prophylaxis or treatment
• Human immunodeficiency virus (HIV) infected patients (if HIV positive)
  • HIV infected individuals are eligible provided they meet all the protocol eligibility criteria in addition to the following:
    • No history of acquired immune deficiency syndrome (AIDS) defining illness other than an historic CD4+ T-cell nadir < 200/mm^3
    • Prior to leukemia diagnosis, the HIV disease was uncomplicated as evidenced by:
      • the CD4+ T-cell counts were generally in excess of 300/mm^3
      • the HIV viral loads were less than 200 copies/ml if on anti-HIV therapy
      • If the HIV is newly diagnosed or there is no history of using anti-HIV therapy, there are no AIDS defining conditions or other HIV-related symptoms
      • Zidovudine is not allowed as part of the anti-HIV therapy
• Patients with diabetes controlled by diet or medication are allowed on trial; controlled diabetes is defined as FBG < 130 mg/kL in the context of this study

Exclusion Criteria:

• Patients who have had chemotherapy or radiotherapy =< 4 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier; treatment with glucocorticoids, hydroxyurea, and tyrosine kinase inhibitors is allowed up to 24 hour prior to initiation of therapy
• Patients with white blood cell (WBC) > 30,000 are not eligible to start therapy; however, it is permissible to use glucocorticoids and/or hydroxyurea to diminish peripheral WBC to less than 30,000 provided these agents are stopped at least 24 hours prior to the first dose of MLN0128 (TAK-228)
• Patients who are receiving any other investigational agents
• Patients with known other active cancers; skin cancers (basal or squamous) are exempted
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to MLN0128 (TAK-228)
• There are no prohibitions of specific medications on the basis of anticipated drug-drug interactions
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, hypertension, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements; no ischemic myocardial or cerebrovascular event, placement of pacemaker, or pulmonary embolism within six months of receiving first dose of MLN0128 (TAK-228)
• Any patient receiving chronic corticosteroid administration prior to study enrollment is ineligible
• Baseline prolongation of the rate-corrected QT interval (QTc) > 480 milliseconds or history of congenital long QT syndrome or Torsades de pointes
• Concomitant administration of any proton pump inhibitor (PPI) is not permitted during the study; patients receiving PPI therapy before enrollment must stop using the PPI for 7 days before their first dose of study drugs