Onvansertib for the Treatment of Recurrent or Refractory Chronic Myelomonocytic Leukemia and Myelodysplastic Syndrome/MPN Overlap Neoplasms

Inclusion Criteria: PRE-REGISTRATION - INCLUSION CRITERIA: * Age \>= 18 years * History of World Health Organization (WHO)-defined diagnosis of proliferative CMML (WBC count \>= 13,000/mm\^3 at time of diagnosis), or MDS/MPN overlap neoplasm with WBC count \>= 13,000/mm3 at time of diagnosis (atypical CML and MDS/MPN-NOS). * NOTE: Hydroxyurea or hypomethylating induced leukopenia does not preclude inclusion. Discussion of WBC \< 13,000/mm\^3 due to treatment at the time of preregistration must be discussed with the Sponsor/Principal Investigator * Relapsed/refractory following treatment with hydroxyurea; or at least 4 cycles of treatment with hypomethylating agents; or who are intolerant of treatment with either therapy. Note: Prior exposure to erythropoiesis stimulating agents is allowed. Hydroxyurea may continue for the first 28 days on study. Continuation of hydroxyurea beyond the first cycle must be discussed with the Sponsor/Principal Investigator * Willing and able to review, understand, and provide written consent before starting any study-specific procedures or therapy * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Willingness to provide mandatory bone marrow specimens for correlative research * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * Recovered to grade 1 or baseline or established as sequelae from all toxic effects of previous therapy except alopecia * Platelet count \>= 20,000/mm\^3 (obtained =\< 14 days prior to pre-registration) * NOTE: For platelet count \< 20,000/mm3 and in situations where the primary investigator deems the thrombocytopenia to be attributable to the underlying CMML, patients can be enrolled as long as they are able to achieve a platelet count of 20,000/mm3 with transfusional support * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (=\< 3 x ULN for patients with Gilbert's syndrome) (obtained =\< 14 days prior to pre-registration) * Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 3 x ULN (obtained =\< 14 days prior to pre-registration) * Estimated glomerular filtration rate (eGFR) \>= 50 mL/min/m\^2 using one of the following methods (obtained =\< 14 days prior to pre-registration): * Chronic Kidney Disease-Epidemiology Collaboration (CKDEPI) 2021 formula * Corrected creatinine clearance via serum and 24-hour urine creatinine assessment * Iothalamate/Iohexol glomerular filtrate rate via plasma/urine assessment * Ability to complete questionnaire(s) by themselves or with assistance * Willingness to provide mandatory blood specimens for correlative research REGISTRATION - INCLUSION CRITERIA: * Histological confirmation of WHO-defined diagnosis of a myelodysplastic/myeloproliferative neoplasm (MDS/MPN) including one of the following (NOTE: to confirm patient is still eligible and has not progressed to AML): * Proliferative CMML * Atypical chronic myeoloid leukemia (aCML) * MDS/MPN not otherwise specified (MDS/MPN, NOS) * NOTE: Hydroxyurea or hypomethylating agent induced leukopenia does not preclude inclusion. Discussion of WBC \< 13,000/mm\^3 due to treatment at the time of registration must be discussed with the Sponsor/Principal Investigator. * For a man or a woman of child-bearing potential (WOCBP): Must agree to use contraception or take measures to avoid pregnancy during the study and for 180 days after the final dose of any study drug. Adequate contraception is defined as follows: * Complete true abstinence * Consistent and correct use of one of the following methods of birth control: * Male partner who is sterile prior to the female patient's entry into the study and is the sole sexual partner for that female patient * Implants of levonorgestrel * Injectable progestogen * Intrauterine device (IUD) with a documented failure rate of less than 1% per year * Oral contraceptive pill (either combined or progesterone only) * Barrier method, for example: diaphragm with spermicide or condom with spermicide in combination with either implants of levonorgestrel or injectable progestogen * WOCBP must have a negative serum or urine pregnancy test =\< 7 days prior to registration * NOTE: WOCBP include any female who has experienced menarche and who has not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or is not postmenopausal (defined as amenorrhea \> 12 consecutive months); or women on hormone replacement therapy with documented serum follicle stimulating hormone (FSH) level \> 35 mIU/mL. Even women who are using oral, implanted or injectable contraceptive hormones or mechanical products such as an IUD or barrier methods (diaphragm, condoms, spermicides) to prevent pregnancy or practicing abstinence or where partner is sterile (eg, vasectomy), must be considered to be of child-bearing potential * NOTE: If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required Exclusion Criteria: PRE-REGISTRATION - EXCLUSION CRITERIA: * Previous exposure to an alternative (investigational) PLK1 inhibitor * Demonstration of transformation to acute leukemia on any prior bone marrow biopsy * Prior allogeneic hematopoietic stem cell transplantation with active grade 2-4 graft-versus-host disease (GVHD) or with moderate to severe chronic GVHD * NOTE: The patient should not have received calcineurin inhibitors ≤28 days prior to pre-registration and should not be actively receiving immunosuppressive therapy for acute or chronic GVHD. * NOTE: CMML or MDS/MPN overlap neoplasms relapse after allogeneic stem cell transplant is allowed as long as they are \>100 days after transplant and do not have the aforementioned GVHD criteria. * Active central nervous system disease * Concurrent active malignancy, except adequately treated nonmelanoma skin cancer. History of curatively treated in situ cancer of the cervix