The purpose of this study is to determine the recommended Phase 2 dose(s) (RP2D[s]) of bleximenib in phase 1 Part 1 (Dose Escalation) and to determine the safety and tolerability at RP2D in Phase 1 Part 2 (Dose expansion). The purpose of the Phase 2 part of the study is to evaluate the efficacy of bleximenib at the RP2D.

Inclusion Criteria:

Phase 1:

• Age 2 years to less than (<) 18 years of age (pediatric cohort only), all other cohorts 18 years and above
• Relapsed or refractory (R/R) acute leukemia and has exhausted, or is ineligible for, available therapeutic options
• Acute leukemia harboring histone-lysine N-methyltransferase 2A (KMT2A), nucleophosmin 1 gene (NPM1) or nucleoporin 98 gene or nucleoporin 214 gene (NUP98 or NUP214) alterations

Phase: 2

• Participants greater than 18 years are eligible
• Must have had an initial diagnosis of acute myeloid leukemia (AML) per the WHO 2022 classification criteria and have relapsed/refractory disease
• AML harboring KMT2A-r (gene rearrangement/translocation) or NPM1 mutations only

For Both Phase 1 and 2:

• Pretreatment clinical laboratory values meeting the following criteria: (a) Hematology: white blood cell (WBC) count <= 20*10^9/liter (L) and (b) renal function; For adult participants, estimated or measured glomerular filtration rate >= 30 milliliter per minute (mL/min) per four variable MDRD equation. For pediatric participants an estimated or measured glomerular filtration rate >=40 mL/min per the CKiD (Chronic Kidney Disease in Children) Schwartz formula
• Eastern Cooperative Oncology Group (ECOG) performance status grade of 0, 1 or 2. Pediatric participants only: Performance status >=70 by Lansky scale (for participants < 16 years of age) or >=70 Karnofsky scale (for participants >=16 years of age)
• A female of childbearing potential must have a negative highly sensitive serum beta-human chorionic gonadotropin at screening and within 48 hours prior to the first dose of study treatment
• Participant must agree to all protocol required contraception requirements and avoid sperm or egg donations or freezing for future reproductive use while on study and for 90 days (males) or 6 months (females) after the last dose of study treatment

Exclusion Criteria:

• Acute promyelocytic leukemia, diagnosis of Down syndrome associated leukemia or juvenile myelomonocytic leukemia according to World Health Organization (WHO) 2016 criteria
• Active central nervous system (CNS) disease
• Prior solid organ transplantation
• QTc according to Fridericia's formula (QTcF) for males >= 450 millisecond (msec) or for females >= 470 msec. Participants with a family history of Long QT syndrome are excluded
• Exclusion criteria related to stem cell transplant: a. Received prior treatment with allogenic bone marrow or stem cell transplant <=3 months before the first dose of study treatment ; b. Has evidence of graft versus host disease; c. Received donor lymphocyte infusion <=1 month before the first dose of study treatment; d. Requires immunosuppressant therapy (exception: daily doses <=10 milligrams (mg) prednisone or equivalent are allowed for adrenal replacement)
• Prior cancer immunotherapy within 4 weeks prior to enrollment or blinatumomab within 2 weeks prior to enrollment. Additional prior cancer therapies must not be given within 4 weeks prior to enrollment or 5 half-lives of the agent (whichever is shorter)

The data sharing policy of Johnson & Johnson Innovative Medicine is available at innovativemedicine.jnj.com/our-innovation/clinical-trials/transparency. As noted on this site, requests for access to the study data can be submitted through Yale Open Data Access (YODA) Project site at yoda.yale.edu