Inclusion Criteria:

          -  Diagnosis of relapsed or refractory AML of any French American British (FAB) subtype
             except M3 and NPM1 genetic mutation detected by molecular assay; AML patients treated
             at Stanford have NPM1 molecular mutation status checked routinely at time of diagnosis
             in a Clinical Laboratory Improvement Amendment (CLIA)-certified laboratory

          -  Male or female patients and no race-ethnic restrictions

          -  Patients are unwilling, or who are determined to be medically unfit for or resistant
             to standard intensive induction chemotherapy; patients who are medically unfit will be
             determined by the treating primary hematologist and the principal investigator
             (including but not limited to evaluation of co-morbidities, and response and
             complications to previous AML treatment strategy)

          -  Eastern Cooperative Oncology Group (ECOG) 0 to 2

          -  Ability to understand and the willingness to sign a written informed consent document

          -  Female patients who:

               -  Are postmenopausal for at least 1 year before the screening visit, OR

               -  Are surgically sterile, OR

               -  If they are of childbearing potential, agree to practice 2 effective methods of
                  contraception, at the same time, from the time of signing the informed consent
                  form through 90 days after the last dose of study drug, AND

               -  Must also adhere to the guidelines of any treatment-specific pregnancy prevention
                  program, if applicable, OR

               -  Agree to practice true abstinence when this is in line with the preferred and
                  usual lifestyle of the subject; (periodic abstinence [eg, calendar, ovulation,
                  symptothermal, post-ovulation methods] and withdrawal are not acceptable methods
                  of contraception)

          -  Male patients, even if surgically sterilized (ie, status post-vasectomy), must agree
             to one of the following:

               -  Agree to practice effective barrier contraception during the entire study
                  treatment period and through 90 days after the last dose of study drug, OR

               -  Must also adhere to the guidelines of any treatment-specific pregnancy prevention
                  program, if applicable, OR

               -  Agree to practice true abstinence when this is in line with the preferred and
                  usual lifestyle of the subject; (periodic abstinence (eg, calendar, ovulation,
                  symptothermal, post-ovulation methods] and withdrawal are not acceptable methods
                  of contraception)

          -  Total bilirubin ≤ 1.5 x the upper limit of the normal range (ULN)

          -  Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3 x ULN

          -  Calculated creatinine clearance ≥ 30 mL/min

        Exclusion Criteria:

          -  Female patient who are lactating or have a positive serum pregnancy test during the
             screening period

          -  Major surgery within 14 days before enrollment

          -  Radiotherapy within 14 days before enrollment; if the involved field is small, 7 days
             will be considered a sufficient interval between treatment and administration of
             MLN9708

          -  Known active and uncontrolled central nervous system (CNS) involvement of leukemia (a
             lumbar puncture does not need to be performed as a part of screening)

          -  Have a significant uncontrolled infection active infection

          -  Have other severe concurrent disease or serious organ dysfunction involving the heart,
             kidney, liver or other organ system that may place the patient at undue risk to
             undergo treatment including uncontrolled hypertension, uncontrolled cardiac
             arrhythmias, symptomatic congestive heart failure, unstable angina, or myocardial
             infarction within the past 6 months

          -  Systemic treatment, within 14 days before the first dose of MLN9708, with strong
             inhibitors of cytochrome P450, family 1, subfamily A, polypeptide 2 (CYP1A2)
             (fluvoxamine, enoxacin, ciprofloxacin), strong inhibitors of cytochrome P450, family
             3, subfamily A (CYP3A) (clarithromycin, telithromycin, itraconazole, voriconazole,
             ketoconazole, nefazodone, posaconazole) or strong CYP3A inducers (rifampin,
             rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital), or use of Ginkgo
             biloba or St. John's wort

          -  Known ongoing or active systemic infection, active hepatitis B or C virus infection,
             or known human immunodeficiency virus (HIV) positive

          -  Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral
             absorption or tolerance of MLN9708 including difficulty

          -  Diagnosed or treated for another malignancy within 2 years before study enrollment or
             previously diagnosed with another malignancy and have any evidence of residual
             disease; patients with nonmelanoma skin cancer or carcinoma in situ of any type are
             not excluded if they have undergone complete resection; this does not preclude
             previous diagnosis of acute myeloid leukemia or myelodysplastic syndrome

          -  Patient has ≥ grade 3 peripheral neuropathy, or grade 2 with pain on clinical
             examination during the screening

          -  Participation in other clinical trials, including those with other investigational
             agents not included in this trial, within 21 days of the start of this trial and
             throughout the duration of this trial

          -  Known allergy to any of the study medications, their analogues, or excipients in the
             various formulations of any agent