Inclusion Criteria:

* Participant must be ≥ 12 years of age at the time of signing the informed consent form (ICF).
* Participant must weigh at least 40 kg
* Participant is willing and able to adhere to the study visit schedule and other protocol requirements.
* Participant has relapsed/refractory acute leukemia defined acute myeloid leukemia, acute lymphoblastic leukemia, or mixed phenotype acute leukemia after as failure of at least 1 prior line of therapy (can be either primary refractory disease or progression during or after treatment)
* Participant has confirmed acute leukemia with detectable NPM1c, KMT2A translocation, or NUP98 translocation.

1. At MSK, NPM1 testing utilizes MSK-REACT, a rapid multi-gene NGS panel used in all new AML diagnoses that is clinically validated by the Laboratory of Diagnostic Molecular Pathology pursuant to the requirements of CLIA'88 and approved by New York State, or MSK-IMPACT, a multi-gene NGS panel, which is authorized by the FDA. At non-MSK sites, NPM1 testing may be performed in local CLIA-certified laboratories using validated clinical assays with capable of detecting NPM1c variants at a frequency of ≥5%. Eligible patients must have an NPM1c (nucleophosmin) exon 12 variant as determined by these assays.
2. At MSK, KMT2A and NUP98 testing will utilize chromosomal analysis and fluorescence in situ hybridization studies. At non-MSK sites, testing may be performed in local CLIA-certified laboratories using validated clinical assays with performance characteristics sufficient to detect relevant translocations. Eligible patients must have a KMT2A or NUP98 translocation as determined by these assays
3. The patient's chart will be utilized for screening purposes
* Regarding prior treatment with a menin inhibitor:

1. Participants enrolled in Phase 1 have no requirements regarding prior treatment with a menin inhibitor
2. Participants enrolled in Phase 2, cohort 1, are required to be menin inhibitor naïve (no previous treatment with a menin inhibitor)
3. Participants enrolled in Phase 2, cohort 2, are required to be menin inhibitor exposed (previous treatment received a menin inhibitor)
* Regarding prior alloSCT, at 60 days must have elapsed from day of transplant and at least 4 weeks must have elapsed from first dose of donor lymphocyte infusion.
* Participant has an Eastern Cooperative Oncology Group (ECOG) performance status score 0-2 (if aged ≥18 years); Karnofsky Performance Scale of ≥50 (if aged ≥16 years and \<18 years); Lansky Performance Score of ≥50 (if aged \<16 years).
* Participant must have a WBC count \<25,000/μL at the time of initiation of study drug (leukapheresis may be performed and/or hydroxyurea may be administered to decrease the WBC count to \<25,000/μL).
* Participant has adequate organ function defined as:

1. Serum aspartate aminotransferase/serum glutamic oxaloacetic transaminase (AST/SGOT) and alanine aminotransferase (ALT/SGPT) ≤ 3 x ULN, unless considered due to leukemic organ involvement.
2. Serum total bilirubin \< 1.5 x ULN. Higher levels are acceptable if these can be attributed to ineffective erythropoiesis, leukemia organ involvement or Gilbert's syndrome.
3. Serum creatinine \< 2 x ULN or estimated glomerular filtration rate 60 mL/min or greater based on local institutional practice for age-appropriate determination (e.g, Schwartz formula for pediatric patients or Cockcroft Gault formula for adults).
4. Adequate cardiac function defined as ejection fraction of ≥ 50% by echocardiogram or multigated acquisition scan.

Exclusion Criteria:

* Participants with acute promyelocytic leukemia
* Participants with isolated myeloid sarcoma
* Participants who have previously received mezigdomide.
* Participants with immediate life-threatening, severe complications of leukemia such as uncontrolled bleeding, pneumonia with hypoxia or shock, disseminated intravascular coagulation, or uncontrolled tumor lysis syndrome.
* Participant has presence of any other condition that may increase the risk associated with study participation, and in the opinion of the treating investigator, would make the patient inappropriate for entry into the study.
* Participants with concurrent other malignancy that will confound interpretation of study endpoints.
* Participants who have received other anti-leukemia therapy within 5 half-lives of the agent or 14 days, whichever is sooner, prior to study treatment and if toxicity related to said agent has not resolved; exceptions of acceptable concomitant therapies are listed below

1. Concomitant cytoreductive therapy in the form of hydroxyurea, corticosteroids, or cytarabine is permitted.
2. Concomitant therapy in the form of intrathecal chemotherapy for CNS treatment, is permitted.
3. Radiation therapy is not permitted except for localized palliative radiation to focal lesions after discussion with the Medical Monitor for patients who have progressed but remain on the study due to perceived clinical benefit per Investigator assessment
* Participants with active graft versus host disease (GVHD) of grade 2 or higher requiring systemic treatment. Skin GVHD solely managed with topical corticosteroids would not be exclusionary.
* Participant has significant active cardiac disease within 6 months prior to start of study treatment, including New York Heart Association (NYHA) class III or IV congestive heart failure; acute coronary syndrome (ACS); and/or stroke.
* Participant has QTc interval (i.e., Fridericia's correction \[QTcF\]) ≥ 450 ms (mean of triplicate ECG) or other factors that increase the risk of QT prolongation or ventricular arrhythmic events (e.g., family history of long QT interval syndrome). Patients with a QTcF over 450 ms due to a bundle branch block or a pacemaker may participate in the study with approval of the study principal investigator.
* Participant has active viral infection with human immunodeficiency virus (HIV), or active infection with hepatitis B virus (HBV) or hepatitis C virus (HCV)
* Participant is known to have dysphagia, short-gut syndrome, gastroparesis, or other conditions that limit the ingestion or gastrointestinal absorption of drugs administered orally.
* Participant has active uncontrolled systemic fungal, bacterial, or viral infection (defined as ongoing signs/symptoms related to the infection without improvement despite appropriate antibiotics, antiviral therapy, and/or other treatment).
* Participant with active use of strong or moderate CYP3A4 inhibitors or strong CYP3A4 inducers. Details reviewed in Appendix B.
* Participant with use of proton pump inhibitors less than 2 weeks prior to initiating treatment
* Female participant who is pregnant or lactating. Male or female participants not willing to comply with contraceptive requirements, which include 4 months of contraception after last dose of revumenib for males and 6 months for females. Additional contraception details reviewed in Appendix D.