Ixazomib, Mitoxantrone Hydrochloride, Etoposide, and Intermediate-Dose Cytarabine in Relapsed or Refractory Acute Myeloid Leukemia

Inclusion Criteria: * Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care * Female patients who: * Are postmenopausal for at least 1 year before the screening visit,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 \[e.g., calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception) * Male patients, even if surgically sterilized (i.e., 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 (e.g., calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception) * Subjects with a prior diagnosis of AML (excluding acute promyelocytic leukemia) based on World Health Organization Classification who did not achieve complete response (CR) with their previous therapy or who have relapsed after achieving a complete response (CR) are eligible; any number of relapses will be eligible. * Patients must have \> 5% blasts in the bone marrow at the time of study enrollment * Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, 2, or 3 * Total bilirubin ≤ 1.5 x the upper limit of the normal range (ULN) within 14 days of enrollment * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3 x ULN within 14 days of enrollment * Calculated creatinine clearance ≥ 30 mL/min within 14 days of enrollment * Patients with secondary AML, and patients with a prior autologous and allogeneic bone marrow transplant are eligible * Patients with an allogeneic transplant must meet the following conditions: the transplant must have been performed more than 90 days before registration to this study, the patient must not have ≥ grade 2 acute graft versus host disease (GvHD) or either moderate or severe limited chronic GvHD, or extensive chronic GvHD of any severity; the patient must be off all immunosuppression for at least 2 weeks * Echocardiogram or multi gated acquisition (MUGA) scan demonstrating an ejection fraction ≥ 45% Exclusion Criteria: * Female patients who are lactating or have a positive serum pregnancy test during the screening period * Failure to have fully recovered (i.e., ≤ grade 1 toxicity) from the reversible effects of prior chemotherapy, excluding alopecia * 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 the MLN9708 * Central nervous system involvement; a lumbar puncture does not need to be performed unless there is clinical suspicion of leptomeningeal disease * Uncontrolled infections * Evidence of current uncontrolled cardiovascular conditions, including uncontrolled hypertension, uncontrolled cardiac arrhythmias, symptomatic congestive heart failure, unstable angina, or myocardial infarction within the past 6 months * Systemic treatment, within 3 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 * Ongoing or active hepatitis B or C virus infection, or known human immunodeficiency virus (HIV) positive * Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol * Known allergy to any of the study medications, their analogues, or excipients in the various formulations of any agent * Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of MLN9708 including difficulty swallowing * Patients with prior malignancy are eligible; however, the patient must be in remission from the prior malignancy and have completed all chemotherapy and radiotherapy at least 6 months prior to registration and all treatment-related toxicities must have resolved; patients with basal cell or squamous cell carcinoma of the skin are eligible regardless of disease status * Patient has ≥ grade 2 peripheral neuropathy within 14 days of trial enrollment * Participation in other clinical trials, including those with other investigational agents not included in this trial, within 14 days of the start of this trial and throughout the duration of this trial * Any standard therapy for leukemia within 14 days before enrollment (except for hydrea) * Patients who have received prior pulmonary radiation