• Phase I - Number of Participants with drug related first-cycle dose limiting toxicities (DLTs) [ Time Frame: Between the date of the first dose administration in Cycle 1 and the date of the first dose administration in Cycle 2 which is expected to be 28 days or up to 42 days in case of dose delay. ]
  DLT is defined as any grade ≥3 non-hematologic toxicity occurring in the first cycle of treatment for which the relationship to NMS-03592088 cannot be definitely excluded, with the exception of:

  • alopecia, anorexia, fatigue;
  • grade 3 infection and fever with neutropenia;
  • grade 3 diarrhea or nausea that did not require tube-feeding or total parenteral nutrition, or diarrhea that could be managed to grade 2 or better with standard drugs.

  Hematological adverse events will not be considered as DLTs. However, prolonged myelosuppresion defined as Grade 4 neutropenia (ANC <500 mm3) after 2-week delay (i.e., 21 days off therapy) in the absence of evidence of active leukemia in the bone marrow or peripheral blood are considered as a DLT. DLTs are classified according to CTCAE version 5.0.
• Phase II - FLT3 mutated AML - Overall Response Rate (ORR) [ Time Frame: From first dose of study drug to End of Treatment (up to 9 months of treatment) ]
  Percentage of Participants with Complete Remission (CR) + Incomplete Hematologic Recovery (CRi) + Morphologic Leukemia-free State (MLFS) + Partial Remission (PR). Responses will be assessed according to the ELN guidelines for Acute Myeloid Leukemia (AML).
• Phase II - CMML - Overall Response Rate (ORR) [ Time Frame: From first dose of study drug to End of Treatment (up to 9 months of treatment) ]
  Percentage of Participants with Complete Remission + Complete Cytogenetic Remission + Partial Remission + Marrow Response + Clinical benefit). Responses will be assessed according to the WHO Criteria for Chronic Myelomonocytic Leukemia (CMML).

• Phase I - Number of Participants with first-cycle dose limiting toxicities (DLTs) [ Time Frame: Between the date of the first dose administration in Cycle 1 and the date of the first dose administration in Cycle 2 which is expected to be 28 days or up to 42 days in case of dose delay. ]
  DLT is defined as any grade ≥3 non-hematologic toxicity occurring in the first cycle of treatment and considered at least possibly related to NMS-03592088, with the exception of:

  • anorexia, fatigue;
  • grade 3 infection and fever with neutropenia;
  • grade 3 diarrhea or nausea that did not require tube-feeding or total parenteral nutrition, or diarrhea that could be managed to grade 2 or better with standard drugs.

  Hematological adverse events will not be considered as DLTs. DLTs will be classified according to CTCAE version 5.0.
• Phase II - FLT3 mutated AML - Overall Response Rate (ORR) [ Time Frame: From first dose of study drug to End of Treatment (up to 9 months of treatment) ]
  Percentage of Participants with Complete Remission (CR) + Incomplete Hematologic Recovery (CRi) + Morphologic Leukemia-free State (MLFS) + Partial Remission (PR). Responses will be assessed according to the ELN guidelines for Acute Myeloid Leukemia (AML).
• Phase II - CMML - Overall Response Rate (ORR) [ Time Frame: From first dose of study drug to End of Treatment (up to 9 months of treatment) ]
  Percentage of Participants with Complete Remission + Complete Cytogenetic Remission + Partial Remission + Marrow Response + Clinical benefit). Responses will be assessed according to the WHO Criteria for Chronic Myelomonocytic Leukemia (CMML).

• Number of participants with Adverse Events (AEs) [ Time Frame: Adverse Events: From the Informed Consent signature to 28 days after the last on-study treatment administration. ]
  Safety will be assessed by AEs, which included abnormalities identified during a medical test (e.g. laboratory tests, vital signs, electrocardiogram, etc.) if the abnormality induces clinical signs or symptoms, needs active intervention, interruption or discontinuation of the study drug or is medically significant. A treatment-emergent AE is defined as abn AE observed after starting administration of the study drug up to 28 days after last dose of study medication intake. AEs will be coded with the Medical Dictionary for Regulatory Activities (MedDRA) and graded according to the The National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE) version 5.0
• Overall Survival (OS) [ Time Frame: From first dose of study drug up to data cut-off (approximately 18 months) ]
  The time from the date of the first dose of study drug until the date of death for any cause. For a participant not known to have died by the end of study follow-up, OS will be censored at the date of the last contact OS will be calculated using Kaplan-Meier estimates.
• Time to Response (TTR) [ Time Frame: From first dose of study drug up to data cut-off (approximately 18 months) ]
  TTR is defined as the time from the first dose of study drug until the date of first response. TTR will be as evaluated for participants who achieved response during treatment, as defined for AML and CMML populations
• Duration of Response [ Time Frame: From date of first remission up to data cut-off (approximately 18 months) ]
  Duration of response was defined as the time from the date of either first CRc or PR until the date of documented relapse of any type for participants who achieved CRc or PR. Participants who died without report of relapse will be considered non-events and censored at their last relapse-free disease assessment date. Other participants who will not relapse on study will be considered non-events and censored at the last relapse-free assessment date. Duration of response will be calculated using Kaplan-Meier method and therefore data will be estimated.
• Relapse-Free Survival (RFS) [ Time Frame: From first dose of study drug up to data cut-off (approximately 18 months) ]
  Duration of response is defined as the time from the date of first dose of study drug until the date of documented relapse/ Progression Disease of any type, as defined for AML and CMML populations. Participants who died without report of relapse will be considered non-events and censored at their last relapse-free disease assessment date. Other participants who will not relapse on study will be considered non-events and censored at the last relapse-free assessment date. Duration of response will be calculated using Kaplan-Meier method and therefore data will be estimated.
• Composite Complete Remission Rate (CRc; CR+CRi+MLFS) [AML population only] [ Time Frame: From first dose of study drug to End of Treatment (up to 9 months of treatment) ]
• Clinical Benefit rate (CBR; CRc + PR + Stable Disease) [AML population only] [ Time Frame: From first dose of study drug to End of Treatment (up to 9 months of treatment) ]
• Maximum concentration (Cmax) of NMS-03592088, NMS-03593860 and NMS-03603422 after single and multiple doses of NMS-03592088 [ Time Frame: Phase I: at Cycle 1 (each cycle is 28 days) and Cycle 2 (schedule A) and at Cycle 1, Cycle 2 and Cycle 3 (schedule B) at different timepoints. Phase II: between predose and 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Time to observed Cmax (Tmax) of NMS-03592088, NMS-03593860 and NMS-03603422 after single and multiple doses of NMS-03592088 [ Time Frame: Phase I: at Cycle 1 (each cycle is 28 days) and Cycle 2 (schedule A) and at Cycle 1, Cycle 2 and Cycle 3 (schedule B) at different timepoints. Phase II: between predose and 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Area under the concentration-time curve to the last measurable concentration (AUClast) of NMS-03592088, NMS-03593860 and NMS-03603422 after single and multiple doses of NMS-03592088 [ Time Frame: Phase I: at Cycle 1 (each cycle is 28 days) and Cycle 2 (schedule A) and at Cycle 1, Cycle 2 and Cycle 3 (schedule B) at different timepoints. Phase II: between predose and 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Terminal elimination half-life (t1/2) of NMS-03592088, NMS-03593860 and NMS-03603422 after multiple doses of NMS-03592088 [ Time Frame: Phase I: at Cycle 1 (each cycle is 28 days) and Cycle 2 at different timepoints, only in schedule A. Phase II: between predose and 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Area under the plasma concentration vs. time curve to infinity (AUCinf) of NMS-03592088, NMS-03593860 and NMS-03603422 after multiple doses of NMS-03592088 [ Time Frame: Phase I: at Cycle 1 (each cycle is 28 days) and Cycle 2 at different timepoints, only in schedule A. Phase II: between predose and 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Accumulation ratio (Rac) of NMS-03592088, NMS-03593860 and NMS-03603422 after multiple doses of NMS-03592088 [ Time Frame: Phase I: at Cycle 1 (each cycle is 28 days) and Cycle 2 (schedule A) and at Cycle 1, Cycle 2 and Cycle 3 (schedule B) at different timepoints. Phase II: between predose and 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Oral plasma clearance (CL/F) of NMS-03592088 after multiple doses of NMS-03592088 [ Time Frame: Phase I: at Cycle 1 (each cycle is 28 days) and Cycle 2 (schedule A) and at Cycle 1, Cycle 2 and Cycle 3 (schedule B) at different timepoints. Phase II: between predose and 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Apparent volume of distribution (Vd/F) of NMS-03592088 after multiple doses of NMS-03592088 [ Time Frame: Phase I: at Cycle 1 (each cycle is 28 days) and Cycle 2 (schedule A) and at Cycle 1, Cycle 2 and Cycle 3 (schedule B) at different timepoints. Phase II: between predose and 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Renal clearance of NMS-03592088, NMS-03593860 and NMS-03603422 after multiple doses of NMS-03592088 [ Time Frame: Phase I at Cycle 1 (each cycle is 28 days) (schedule A) and at Cycle 1 and Cycle 2 (schedule B) at different timepoints. ]
  In patients enrolled starting from dose level 6 and treated following schedule A, urine will be collected at Day 1 Cycle 1 (predose) and during 24 hour-period after drug intake at Cycle 1, Day 21. In patients enrolled starting from the first dose level and treated following schedule B, urine will be collected at Day 1 Cycle 1 (predose) and during 24 hour-period after drug intake at Cycle 1, Day 28. Samples of urine will be used for pharmacokinetics assessments.

• Number of participants with Adverse Events (AEs) [ Time Frame: Adverse Events: From the Informed Consent signature to 28 days after the last on-study treatment administration. ]
  Safety will be assessed by AEs, which included abnormalities identified during a medical test (e.g. laboratory tests, vital signs, electrocardiogram, etc.) if the abnormality induces clinical signs or symptoms, needs active intervention, interruption or discontinuation of the study drug or is medically significant. A treatment-emergent AE is defined as abn AE observed after starting administration of the study drug up to 28 days after last dose of study medication intake. AEs will be coded with the Medical Dictionary for Regulatory Activities (MedDRA) and graded according to the The National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE) version 5.0
• Overall Survival (OS) [ Time Frame: From first dose of study drug up to data cut-off (approximately 18 months) ]
  The time from the date of the first dose of study drug until the date of death for any cause. For a participant not known to have died by the end of study follow-up, OS will be censored at the date of the last contact OS will be calculated using Kaplan-Meier estimates.
• Time to Response (TTR) [ Time Frame: From first dose of study drug up to data cut-off (approximately 18 months) ]
  TTR is defined as the time from the first dose of study drug until the date of first response. TTR will be as evaluated for participants who achieved response during treatment, as defined for AML and CMML populations
• Duration of Response [ Time Frame: From date of first remission up to data cut-off (approximately 18 months) ]
  Duration of response was defined as the time from the date of either first CRc or PR until the date of documented relapse of any type for participants who achieved CRc or PR. Participants who died without report of relapse will be considered non-events and censored at their last relapse-free disease assessment date. Other participants who will not relapse on study will be considered non-events and censored at the last relapse-free assessment date. Duration of response will be calculated using Kaplan-Meier method and therefore data will be estimated.
• Relapse-Free Survival (RFS) [ Time Frame: From first dose of study drug up to data cut-off (approximately 18 months) ]
  Duration of response is defined as the time from the date of first dose of study drug until the date of documented relapse/ Progression Disease of any type, as defined for AML and CMML populations. Participants who died without report of relapse will be considered non-events and censored at their last relapse-free disease assessment date. Other participants who will not relapse on study will be considered non-events and censored at the last relapse-free assessment date. Duration of response will be calculated using Kaplan-Meier method and therefore data will be estimated.
• Composite Complete Remission Rate (CRc; CR+CRi+MLFS) [AML population only] [ Time Frame: From first dose of study drug to End of Treatment (up to 9 months of treatment) ]
• Clinical Benefit rate (CBR; CRc + PR + Stable Disease) [AML population only] [ Time Frame: From first dose of study drug to End of Treatment (up to 9 months of treatment) ]
• Maximum concentration (Cmax) of NMS-03592088 and NMS-03593860 after single and multiple doses of NMS-03592088 [ Time Frame: Phase I, dose escalation -Day 1, Cycle 1: predose, 0.5, 1, 2, 4, 6 and 24 hours; dose escalation and expansion Day21, Cycle 1,: predose, 0.5, 1, 2, 4, 6, 24 and 96 hours. Phase II: on selected time points between predose and 24 or 48 or 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Time to observed Cmax (Tmax) of NMS-03592088 and NMS-03593860 after single and multiple doses of NMS-03592088 [ Time Frame: Phase I, dose escalation -Day 1, Cycle 1: predose, 0.5, 1, 2, 4, 6 and 24 hours; dose escalation and expansion Day21, Cycle 1,: predose, 0.5, 1, 2, 4, 6, 24 and 96 hours. Phase II: on selected time points between predose and 24 or 48 or 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Area under the concentration-time curve to the last measurable concentration (AUClast) of NMS-03592088 and NMS-03593860 after single and multiple doses of NMS-03592088 [ Time Frame: Phase I, dose escalation -Day 1, Cycle 1: predose, 0.5, 1, 2, 4, 6 and 24 hours; dose escalation and expansion Day21, Cycle 1,: predose, 0.5, 1, 2, 4, 6, 24 and 96 hours. Phase II: on selected time points between predose and 24 or 48 or 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Terminal elimination half-life (t1/2) of NMS-03592088 and NMS-03593860 after multiple doses of NMS-03592088 [ Time Frame: Phase I, dose escalation and expansion - Day 21, Cycle 1: predose, 0.5, 1, 2, 4, 6, 24 and 96 hours. Phase II: on selected time points between predose and 24 or 48 or 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Area under the plasma concentration vs. time curve to infinity (AUCinf) of NMS-03592088 and NMS-03593860 after multiple doses of NMS-03592088 [ Time Frame: Phase I, dose escalation and expansion - Day 21, Cycle 1: predose, 0.5, 1, 2, 4, 6, 24 and 96 hours. Phase II: on selected time points between predose and 24 or 48 or 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Accumulation ratio (Rac) of NMS-03592088 and NMS-03593860 after multiple doses of NMS-03592088 [ Time Frame: Phase I, dose escalation - Day 1, Cycle 1: predose, 0.5, 1, 2, 4, 6 and 24 hours; Day 21, Cycle 1: predose, 0.5, 1, 2, 4, 6, 24 and 96 hours. Phase II: on selected time points between predose and 24 or 48 or 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Oral plasma clearance (CL/F) of NMS-03592088 after multiple doses of NMS-03592088 [ Time Frame: Phase I, dose escalation and expansion - Day 21, Cycle 1: predose, 0.5, 1, 2, 4, 6, 24 and 96 hours. Phase II: on selected time points between predose and 24 or 48 or 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Apparent volume of distribution (Vd/F) of NMS-03592088 after multiple doses of NMS-03592088 [ Time Frame: Phase I, dose escalation and expansion - Day 21, Cycle 1: predose, 0.5, 1, 2, 4, 6, 24 and 96 hours. Phase II: on selected time points between predose and 24 or 48 or 96 hours. ]
  Plasma samples will be collected and used for pharmacokinetics assessments.
• Renal clearance of NMS-03592088 and NMS-03593860 after multiple doses of NMS-03592088 [ Time Frame: Phase I, dose escalation and expansion - Day 1, Cycle 1: predose; Day 21, Cycle 1: 0-8 and 8-24 hours postdose. Day 21 is the last day of study drug intake; each cycle is 28 days. ]
  In patients enrolled after the first DLT occurrence, urine will be collected at Day 1 Cycle 1 (predose) and during 24 hour-period after drug intake at Cycle 1, Day 21. Samples of urine will be used for pharmacokinetics assessments.

• Acute Myeloid Leukemia (AML)
• Chronic Myelomonocytic Leukemia (CMML)

• Experimental: Dose Escalation and Expansion (Phase I)
  Dose escalation will be applied until one patient experiences first cycle DLT (Dose Limiting Toxicity) or 2 patients at any dose level experience non-DLT NCI CTCAE Grade ≥2 drug-related toxicity during the first cycle. Once the Maximum Tolerated Dose (MTD) is identified, a maximum of 10 additional patients will be enrolled (dose expansion).
  Intervention: Drug: NMS-03592088
• Experimental: AML FLT3 mutated (Phase II)
  Cohort of AML FLT3 mutated patients. NMS-03592088 will be administered at the recommended Phase II dose (RP2D) defined in Phase I part.
  Intervention: Drug: NMS-03592088
• Experimental: CMML (Phase II)
  Cohort of patients with CMML. NMS-03592088 will be administered at the recommended Phase II dose (RP2D) defined in Phase I part.
  Intervention: Drug: NMS-03592088

Inclusion Criteria:

Phase I:

1. Patients with relapsed/refractory disease who have failed standard therapy or are unsuitable for standard treatment, with one the following confirmed diagnosis:

   • AML as defined by the 2017 European LeukemiaNet (ELN) recommendations
   • CMML as defined by the World Health Organization (WHO) criteria.

   Phase II:

2. Cohort 1 (FLT3 mut AML):

   • Patients with confirmed diagnosis of AML as defined by the 2017 ELN recommendations positive for FLT3 internal tandem duplication (ITD) and/or tyrosine kinase domain (TKD) point mutations in the bone marrow (BM) or peripheral blood (PB) as determined by the local standard test performed at study entry. Patients with an allelic frequency ≥10% will be considered to have FLT3-ITD-mutated disease.
   • Patients must be refractory to at least 1 cycle of induction chemotherapy or relapsed after achieving remission with a prior therapy or unsuitable to receive standard therapy due to age, comorbidities or other factors.
   • Prior treatment with a FLT3 inhibitor is allowed.

3. Cohort 2 (CMML):

   • Patients with confirmed diagnosis of CMML, as defined by WHO criteria who have failed previous therapies or are unsuitable to receive standard therapy due to age, comorbidities or other factors.

   Applying to both Phase I and Phase II:

4. Adult (age > or = 18 years) patients
5. Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2
6. The interval from prior antitumor treatment to time of NMS-03592088 administration should be at least 2 weeks for any agents other than hydroxyurea.
7. All acute toxic effects (excluding alopecia) of any prior therapy must have resolved to NCI CTCAE version 5.0 Grade ≤1
8. Adequate hepatic function.
9. Adequate renal function.
10. Patients must use effective contraception. Female patients must be surgically sterile or be postmenopausal, or must agree to the use of effective contraception during the period of therapy and in the following 90 days after discontinuation of study treatment. Male patients must be surgically sterile or must agree to use effective contraception during the period of therapy and in the following 90 days after discontinuation of study treatment.
11. Capability to swallow capsules intact (without chewing, crushing, or opening)
12. Willingness and ability to comply with scheduled visits, treatment plan, laboratory tests and other study indications or procedures
13. Signed and dated Institutional Review Board/Ethic Committee (IRB/EC)-approved informed consent form indicating that the patient is aware of the neoplastic nature of his/her disease and has been informed of the procedures to be followed, the investigational nature of the therapy, potential benefits, side effects, discomforts, risks and alternative treatments.

Exclusion Criteria:

1. Current enrollment in another interventional clinical study
2. Diagnosis of acute promyelocytic leukemia or breakpoint cluster region-Abelson (BCR-ABL)-positive leukemia
3. Currently active second malignancy, except for adequately treated basal or squamous cell skin cancer and/or cone biopsied in situ carcinoma of the cervix uteri and/or superficial bladder cancer.
4. Patients with known leukemia involvement of CNS
5. Hematopoietic stem cell transplantation (HSCT) within 3 months of treatment start and/or persistent non-hematologic toxicities of Grade ≥2 related to the transplant.
6. Active acute or chronic graft versus host disease (GVHD) requiring immunosuppressive treatment
7. Patients with QTcF interval ≥ 480 milliseconds or with risk factors for torsade de pointes (e.g., uncontrolled heart failure, uncontrolled hypokalemia, history of prolonged QTc interval or family history of long QT syndrome). For patients receiving treatment with concomitant medications known to prolong the QTc interval, replacement with another treatment needs to be considered. If replacement or discontinuation is not clinically feasible, a careful risk/benefit evaluation should be performed prior to enrollment.
8. Pregnancy. All female patients with reproductive potential must have a negative pregnancy test (serum or urine) within the screening period prior to start of study drug.
9. Breast-feeding or planning to breast feed during the study or within 3 months after study treatment.
10. Known hypersensitivity to any of the components of the NMS-03592088 drug product.
11. Any of the following in the previous 6 months: myocardial infarction, unstable angina, coronary/peripheral artery bypass graft, symptomatic congestive heart failure, cerebrovascular accident or transient ischemic attack, pulmonary embolism, deep vein thrombosis
12. Known active, life threatening or clinically significant uncontrolled systemic infection.
13. Known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS)-related illness
14. Active Hepatitis B Virus (HBV) or Hepatitis C Virus (HCV) C infection.
15. Known active gastrointestinal disease (e.g., Crohn's disease, ulcerative colitis, or short gut syndrome) or other malabsorption syndromes that would impact on drug absorption.
16. Known active gastrointestinal ulcer
17. Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that may increase the risk associated with study participation or study drug administration or may interfere with the interpretation of study results and, in the judgment of the Investigator, would make the patient inappropriate for entry into this study or could compromise protocol objectives in the opinion of the Investigator and/or the Sponsor.