Inclusion Criteria:
* Age ≥16 years during dose escalation portion of study, patients must weigh ≥40 kg.
* Age \>12 years during dose expansion portion of study, patients must weight ≥40 kg.
* Diagnosis of AML per the WHO Classification of Hematolymphoid Tumors (5th Edition) with documented KMT2A rearrangement or NPM1 cytoplasmic-type (NPM1c) mutation. KMT2A-rearrangements must be confirmed by FISH or RNA-based fusion calling by a CLIA-certified laboratory. This study will only enroll KMT2A gene rearrangements in which there is a translocation between the N-terminal portion of KMT2A and a fusion partner, and will not include KMT2A partial tandem duplications (PTDs) or other structural alterations of KMT2A. NPM1c mutations must be confirmed by DNA sequencing in a CLIA-certified laboratory. Patients with myeloid sarcoma are eligible only if concurrent bone marrow involvement is present. Patients must have at least 5% bone marrow disease by morphology at the time of study entry.
* Patients with NPM1 mutated AML must either be FLT3 ITD wild type or have an ITD allelic ratio of \<0.05 (i.e. not eligible for a targeted FLT3 tyrosine kinase inhibitor).
* Patients must have relapsed or be refractory to at least one prior line of conventional therapy for AML or MDS-AML.
* Eastern Cooperative Oncology Group (ECOG) performance status must be 0, 1, or 2; Karnofsky ≥50 for patients ≥16 years of age; and Lansky ≥50 for patients ≥12 to 16 years of age.
* Participants must meet the following organ and marrow function as defined below:
* Leukocytes \<25,000/mcL (hydroxyurea, leukapheresis, or single dose of cytarabine 1 g IV are permitted to meet this criterion)
* AST(SGOT)/ALT(SGPT) ≤5 × institutional ULN and total bilirubin ≤ 2x institutional ULN unless related to leukemic involvement or known Gilbert's syndrome (for bilirubin).
* Cardiac LVEF of ≥40%, as measured by echocardiogram or MUGA scan
* Glomerular filtration rate (GFR)≥30 mL/min/1.73 m2
* The patient, a parent (if the patient is \<18 years old), or a legally authorized representative must be able to understand and provide informed consent.
* Patients of childbearing potential are eligible for the study but must comply with the pregnancy prevention plan for study drugs. See Appendix B for details.
* Patient's life expectancy attributed to AML must be greater than 3 months.
* Participants 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. Life expectancy attributed to malignancy other than AML must be greater than 24 months. Patients with concurrent malignancy who are receiving chemotherapy or whose disease is uncontrolled or progressing are not eligible.
Exclusion Criteria:
* AML diagnosis without KMT2A-rearrangement or NPM1-mutation. KMT2A-PTD patients and patients with KMT2A alterations other than translocations are excluded.
* Active central nervous system (CNS) involvement by AML (i.e., CNS-2 or CNS-3 disease). Previously treated CNS disease or those receiving prophylactic intrathecal chemotherapy per institutional standard is allowed.
* Myeloid sarcoma or extramedullary disease without bone marrow disease.
* Participants who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> Grade 1 by the NCI-CTCAE version 5.0) with the exception of alopecia.
* Participants who are receiving any other investigational agents for this condition.
* Clinically active HIV disease.
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to mezigdomide (i.e. lenalidomide, thalidomide)
* Patient received chemotherapy, immunotherapy, radiation therapy, or ancillary therapy that is considered to be investigational \<7 days prior to the first dose of ziftomenib and mezigdomide, or within 5 drug half-lives prior to the first dose of study drug, whichever is longer.
* Patients with psychiatric, familial, or geographic factors that may impede ability to provide informed consent, to follow study protocol, or hamper study compliance.
* Any other significant medical or psychosocial comorbidities that would preclude the patient from participating in the study or would confound interpretation of study results.
* Patients with the following uncontrolled comorbidities will be excluded: symptomatic congestive heart failure (NYHA class 3 or higher), unstable angina pectoris, serious cardiac arrhythmia as uncontrolled ventricular arrhythmias, electrocardiographic evidence of acute ischemia (type 1 NSTEMI), active, uncorrected conduction abnormalities as Mobitz 2 or third degree heart block (not excluded if pacemaker placed), myocardial infarction with evidence of residual abnormalities within 6 months prior to enrollment. An elevation in troponin is not an exclusion criterion if there are no evidence of residual cardiac dysfunction or ongoing ischemic event. Patients with congenital conduction abnormalities as Wolff-Parkinson White, long QT syndrome, or Brugada syndrome may be eligible with consultation of cardiology confirming stability.
* Mean corrected QT interval corrected for heart rate by Frederica's formula (QTcF)\>480ms.
* Patients on dialysis.
* Patients with active infection that are deemed controlled will be permitted to enroll. Patients with uncontrolled infection may enroll once infection is treated and brought under control.
* Subjects who have undergone a hematopoietic stem cell transplant (HSCT) within 90 days of the first dose of treatment on study, or subjects on immunosuppressive therapy post HSCT at the time of screening, or with clinically significant graft-versus-host disease (GVHD), requiring an equivalent dose of ≥ 0.5mg/kg/day of prednisone or therapy beyond systemic corticosteroids. (The use of topical steroids for ongoing skin GVHD is permitted.)
* Patients who are unable to swallow pills.
* Patient with gastrointestinal disease or surgery (e.g., gastric bypass surgery) that may significantly alter the absorption of mezigdomide and/or other oral study treatment.
* Proton pump inhibitors and potassium-competitive acid blockers are not permitted due to limited absorption of mezigdomide if the stomach is not acidic; a 7-day washout is required prior to start of study treatment.
* Has active Hepatitis B or C
