• Diagnosis of AML or MDS with increased blasts (MDS-IB) assessed by local laboratory review according to the 2022 World Health Organization (WHO) criteria for myeloid neoplasms. Both patients with MDS-IB1 (5-9% bone marrow blasts) and MDS-IB2 (10-19% bone marrow blasts) are eligible.

• Patients must have relapsed or refractory disease after receiving at least one prior line of therapy

• AML-specific inclusion criteria: Patients with relapsed or refractory AML with \>= 5% bone marrow blasts after receiving at least two courses of intensive induction chemotherapy (including, but not limited to, 7+3 regimen, fludarabine, cytarabine, idarubicin and filgrastim \[FLAG-Ida\] and mitoxantrone, etoposide, and cytarabine \[MEC\]) or 2 cycles of venetoclax-based lower intensity regimen (azacitidine plus venetoclax or low-dose cytarabine plus venetoclax), and without any other approved therapies available that would be more appropriate in the investigator's judgment. Patients who have received only one course of intensive induction chemotherapy but are not eligible for a second course because of decreased performance status or clear disease progression may be eligible for participation after discussion with the study principal investigator (PI). Patients with concomitant extramedullary disease relapse are eligible to participate, but not patients with isolated extramedullary relapse without bone marrow disease.

• MDS-specific inclusion criteria: Patients with relapsed or refractory MDS-IB with \>= 5% bone marrow blasts after at least 4 cycles of hypomethylating agent (HMA)-based therapy or at least two courses of intensive induction chemotherapy and meet criteria for stable disease (SD), progressive disease (PD) or disease relapse according to the International Working Group 2023 response criteria for higher-risk MDS. Patients must not have access to any other approved therapies that would be more appropriate in the investigator's judgment. Patients who have received less than 4 cycles of HMA-based therapy may be eligible to participate after discussion with the study PI if there is clear evidence of progression or intolerance to HMA-based therapy that precludes its continuation.

• Patients must have recovered from the effects of any prior systemic therapy, radiotherapy or surgery:

‣ Patients should not have received other investigational therapy within 2 weeks.

⁃ Patients should not have received standard chemotherapy within 1 week of administration of study drug; hydroxyurea administration (for leukocyte count control) is permitted.

• Age \>=18 years. Because no dosing or adverse event data are currently available on the use of TAK-243 in patients \<18 years of age, children are excluded from this study.

• Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 50%).

• Serum bilirubin =\< 1.5 × institutional upper limit of normal (ULN).

‣ Patients with a known history of Gilbert's syndrome may enroll.

• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 × institutional ULN.

• Serum creatinine \< 176 mcmol/L (2 mg/dL) OR

• Creatinine clearance \> 60 mL/min based on the Cockcroft-Gault equation.

• Documented normal cardiac function (\>= 50%) by echocardiogram or multi-gated acquisition (MUGA) scan.

• HIV-infected patients on effective anti-retroviral therapy with undetectable viral load withing 6 months are eligible for this trial.

• For patients with evidence of chronic hepatitis B virus (HBV) infection, HBV viral load must be undetectable on suppressive therapy if indicated.

• Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load.

• The effects of TAK-243 on the developing human fetus are unknown and ubiquitin-activating enzyme inhibitors are known to be teratogenic. For this reason, female patients must be:

‣ Postmenopausal (age-related amenorrhea \>= 12 consecutive months or follicle-stimulating hormone \> 40 mIU/mL), for at least 1 year before the screening visit, OR

⁃ Surgically sterile (i.e., who had undergone hysterectomy or bilateral oophorectomy), OR

∙ If they are of childbearing potential:

• Agree to practice 1 highly effective method and 1 additional effective (barrier) method of contraception, at the same time, from the time of signing the informed consent through 4 months after the last dose of study drug (female and male condoms should not be used together), OR

• Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the patient. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.) Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.

‣ Male patients, even if surgically sterilized (i.e., status post-vasectomy), who:

• Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug (female and male condoms should not be used together), OR

• Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods for the female partner\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.)

‣ Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants.

⁃ Patients should have a minimum life expectancy of 1 month.