Inclusion Criteria:
* An established and confirmed diagnosis of AML by World Health Organization criteria, excluding acute promyelocytic leukemia (APL) (with promyelocytic leukemia -retinoic acid receptor alpha \[PML-RARA\])
* Patients with R/R AML, defined as:
* Relapsed: \>= 5% bone marrow blasts by morphology, reappearance of peripheral blood blasts, or development of extramedullary leukemia after achieving prior CR or CRi. First or second relapse is eligible. First relapse is restricted to participants with CR 1 duration of less than 9-12 months
* Refractory: no CR or CRi after one or more cycles of induction. Induction cycles include regimens with the intent to achieve remission and can include high intensity and/or low intensity regimens
* Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of M3814 in combination with mitoxantrone, etoposide, and cytarabine in patients \< 18 years of age, children are excluded from this study, but will be eligible for future pediatric trials
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (or Karnofsky \>= 60%)
* Serum bilirubin =\< 1.5 institutional upper limit of normal (ULN) (For patients with hemolysis, Gilbert's syndrome or liver infiltration with leukemia, serum bilirubin =\< 3 x institutional ULN)
* Aspartate aminotransferase (AST)(serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional ULN (For patients with liver infiltration with leukemia, AST\[SGOT\]/ALT\[SGPT\] =\< 5 x institutional ULN)
* Glomerular filtration rate (GFR) \>= 60 mL/min/1.73 m\^2 using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formula
* Patients must be medically eligible to receive MEC, including acceptable pre-study cardiac function (left ventricular ejection fraction of \>= 45%) and lifetime anthracycline exposure (=\< 360 mg/m\^2 daunorubicin equivalents)
* Patients may have had prior allogeneic hematopoietic cell transplant at least 3 months prior to enrollment but should not have evidence of active graft versus host disease or require systemic immune suppression
* Patients must be willing to submit the blood sampling and bone marrow sampling for any mandatory PK and pharmacodynamics analyses and exploratory biomarkers
* Female patients with child bearing potential must have a negative serum pregnancy test within 72 hours prior to the first study drug administration and all patients must be willing to use effective methods of contraception during the treatment period and 3 months after study completion
* Human immunodeficiency virus (HIV)-infected patients will be eligible for this trial if they are on effective antiretroviral regimens utilizing non-CYP-interacting agents, they have an undetectable viral load, they have a CD4 count \> 350 cells/mm\^3, and they have no history of acquired immune deficiency syndrome (AIDS)-defining opportunistic infections. If there is evidence of chronic hepatitis B virus (HBV) infection, HBV viral load must be undetectable on suppressive therapy, if indicated. If there is history of hepatitis C virus (HCV) infection, the patient must have been treated and have undetectable HCV viral load
* Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial
* Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity (IDMC) who have a legally-authorized representative (LAR) and/or family member available will also be eligible
* All non-hematologic adverse events (AEs) of prior chemotherapy, surgery, or radiotherapy, except alopecia, must have resolved to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) grade =\< 1 prior to starting therapy
Exclusion Criteria:
* Patients must not have had prior treatment with MEC
* Patients must not have documented active central nervous system (CNS) involvement by leukemia. Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events (AEs)
* Patients must not have received any other investigational or commercial agents or therapies administered with the intention to treat their leukemia within 14 days or 5 elimination half-lives (whichever is shorter) of first receipt of study drug, with the exception of hydroxyurea and/or leukapheresis used to control white blood cell counts
* Patients who cannot discontinue concomitant medications or herbal supplements that are strong inhibitors or strong inducers of cytochrome P450 (CYP) isoenzymes CYP3A4/5, CYP2C9 and CYP2C19 during treatment with M3814. Concomitant use of CYP1A2, CYP2B6 and CYP3A4/5 substrates with a narrow therapeutic index are also excluded during treatment with M3814. Patients may confer with the study doctor to determine if alternative medications can be used. The following categories of medications and herbal supplements must be discontinued for at least the specified period of time prior to the first dose of M3814:
* Strong inducers of CYP3A4/5, CYP2C9 and CYP2C19: \>= 3 weeks or 5 elimination half-lives (whichever is shorter) prior to the first dose of M3814
* Strong inhibitors of CYP3A4/5, CYP2C9 and CYP2C19: \>= 1 week or 5 elimination half-lives (whichever is shorter) prior to the first dose of M3814
* Substrates of CYP1A2, CYP2B6 and CYP3A4/5 with a narrow therapeutic index: \>= 1 day prior to the first dose of M3814
* Concomitant use of histamine-2 (H2)-blockers or proton pump inhibitors should be avoided as these might affect absorption of M3814; administrations have to be discontinued at least 5 days or 5 elimination half-lives (whichever is shorter) prior to the first dose of M3814. Antacid drugs should not be taken 1 hour before and until 2 hours after M3814 administration
* Patients receiving sorivudine or any chemically related analogues (such as brivudine) are excluded
* Patients who require oral or parenteral anticoagulants or thrombolytic agents for therapeutic purposes (including coumadin and warfarin), or who received such agents within 5 days or 5 elimination half-lives (whichever is shorter) of the first dose of M3814. Low and high-molecular weight heparins are permitted provided the platelets are maintained at greater than 30,000/mm\^3
* Patients with ongoing active infection or who have received a live attenuated vaccine within 30 days of dosing with M3814
* Patients must not have known significant cardiopulmonary disease defined as:
* Unstable angina;
* Congestive heart failure (New York Heart Association \[NYHA\] class III or IV);
* Myocardial infarction (MI) within 6 months prior to first dose. Patients who had ischemic heart disease such as acute coronary syndrome (ACS), MI, and/or revascularization more than 6 months before screening and who are without cardiac symptoms or those with a prior non-ST elevation MI (NSTEM) due to demand-supply mismatch (NSTEM Type II) may enroll
* Patients should not have severe and/or uncontrolled medical conditions or other conditions that, in the opinion of the investigator, could affect their participation in the study
* Patients with psychiatric illness/social situations that would limit compliance with study requirements
* Patients should not be pregnant or breastfeeding
* A marked baseline prolongation of QT/corrected QT (QTc) interval (e.g., repeated demonstration of a QTc interval \> 480 milliseconds \[ms\] \[CTCAE grade 2\] using Fredericia's QT correction formula)
* A history of additional risk factors for TdP (e.g., heart failure, hypokalemia, family history of Long QT syndrome)
* The use of concomitant medications that prolong the QT/QTc interval
* Gastrointestinal disorders that may affect the M3814 absorption
* Patients will need to avoid any intake of grapefruit, grapefruit juice, Seville oranges, Seville orange marmalade, or other products containing grapefruit or Seville oranges within 7 days before the first administration of M3814 and throughout the duration of M3814 treatment
