Core criteria: - Adequate organ function. - Contraceptive use by participants or participant partners should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies. Module 1: - Advanced haematologic malignancy - a) for dose escalation - diagnosis of acute leukemia or myelodysplastic neoplasia (MDS) and harbouring one of the genetic alterations per local testing associated with upregulation of HOX; b) for Backfill - diagnosis of harbouring a KMT2Ar or NPM1m per local testing. - Participants must have measurable disease that is relapsed/refractory to conventional therapies known to be effective for their disease and not have any available approved therapies.: a) Relapsed and primary refractory acute leukaemia after standard of care therapy including but not limited to 2 cycles of intensive chemotherapy, hypomethylating agent (HMA) monotherapy, or HMA combinations such as HMA/venetoclax.; b) Relapsed and primary refractory MDS is defined by ≥ 5% blasts in the bone marrow and/or persistence of peripheral blasts after treatment with at least 2 cycles of HMA. Participants ineligible for the treatment with an HMA and without any other standard of care (SoC) options are allowed to enrol; c) White blood cell count below 25,000/μL. Participants may receive cytoreduction per protocol-specified criteria; d) Performance status: Eastern Cooperative Operative Group (ECOG) ≤ 2; e) Life expectancy: ≥ 8 weeks. Module 2: - Participants must have measurable disease that is relapsed/refractory to conventional therapies known to be effective for their disease and not have any available approved therapies.: a) Relapsed and primary refractory acute leukaemia after standard of care therapy including but not limited to 2 cycles of intensive chemotherapy, HMA monotherapy, or HMA combinations such as HMA/venetoclax.; b) Relapsed and primary refractory MDS is defined by ≥ 5% blasts in the bone marrow and/or persistence of peripheral blasts after treatment with at least 2 cycles of HMA. Participants ineligible for the treatment with an HMA and without any other SoC options are allowed to enrol; c) White blood cell count below 25,000/μL. Participants may receive cytoreduction per protocol-specified criteria; d) Performance status: ECOG ≤ 2; e) Life expectancy: ≥ 8 weeks.

Core criteria: - Participants with Burkitt lymphoma/leukaemia or Acute Promyelocytic Leukaemia. - Active testicular or active central nervous system (CNS) (> CNS1 or radiographic) involvement by leukaemia. - Unresolved treatment-related toxicities Grade ≥ 2 from prior therapy. - Abnormal levels of potassium or magnesium prior to first dose of AZD3632. Module 1: - Receipt of non-CNS radiation therapy within 2 weeks and of CNS radiation within 8 weeks of the first scheduled dose. - Receipt of any investigational or non-investigational anticancer agents, including non-biologic agents, biologic agents and/or prior treatment other menin inhibitors (backfill participants only). - For nested food effect participants - diagnosis of diabetes mellitus (Type I or Type II). Module 2: - Receipt of any non-investigational anticancer agents, including non-biologic agents and/or biologic agents or receipt of non-CNS or CNS radiation therapy. - Participants for whom treatment with posaconazole is contraindicated per the local prescribing information.