Tagraxofusp to Eradicate Measurable Residual Disease in Patients With Acute Myeloid Leukemia

Inclusion Criteria:

* Age \>= 18 years
* AML in first or second remission, including:

  * Complete remission (CR), defined as bone marrow blasts \< 5%, absence of circulating blasts, absence of extramedullary disease, absolute neutrophil count (ANC) \>= 1,000/uL, platelet count \> 100,000/uL
  * Complete remission with incomplete hematologic recovery (CRi), defined as all CR criteria except for residual neutropenia (ANC \< 1,000/uL) or residual thrombocytopenia (platelet count \< 100,000/uL)
  * Morphologic leukemia-free state with adequate marrow recovery, defined as bone marrow blasts \< 5%, ANC \>= 500/uL, and platelet count \>= 20,000/uL
* Minimal residual disease positive \>= 0.01% based on MPFC

  * For participants in first remission, MRD positivity at any point from time of establishing first remission onward while still in first remission
  * For participants in second remission, MRD positivity at any point from time of establishing second remission onward while still in second remission
  * MRD must be repeated and remain positive if additional treatment is given prior to enrollment
* CD123 positivity on flow cytometry (partial, dim, or bright) from either:

  * Conventional flow cytometry on marrow specimen from time of original diagnosis or first relapse
  * High-sensitivity multiparametric flow cytometry on marrow specimen from time of MRD positivity
* Eastern Cooperative Oncology Group (ECOG) 0-2
* Serum albumin level \>= 3.2 g/dL in the absence of receiving albumin infusion
* Serum total bilirubin =\< 1.5 mg/dL, unless considered due to Gilbert's disease or medication effect
* Aspartate aminotransferase (AST), alanine aminotransferase (ALT), and alkaline phosphatase =\< 2.5 times the upper limit of normal, unless considered due to medication effect (eg, azole therapy)
* Creatinine clearance \>= 60 mL/min based on Cockcroft-Gault glomerular filtration rate (GFR) and serum creatinine (Cr) =\< 1.8 mg/dL
* Ability to give full informed consent
* Females of reproductive potential (postmenopausal for less than 24 consecutive months) must have a negative pregnancy test within 1 week of initiating treatment and may not be breastfeeding

Exclusion Criteria:

* MRD negativity \< 0.01% at screening
* Intensive AML therapy within the past 14 days, or non-intensive targeted therapy within the past 7 days
* Cord blood as donor source
* Second malignancy that would be expected to limit survival within less than 2 years
* Cardiovascular disease that would result in high risk for toxicity, including:

  * Uncontrolled or New York Heart Association (NYHA) class III or VI congestive heart failure
  * Recurrent or uncontrolled angina
  * Unstable angina, myocardial infarction, or stroke in past 6 months
  * Uncontrolled hypertension
  * Arrhythmia not controlled by medication
* Left ventricular ejection fraction \< 50%
* History of coronary stent placement that requires mandatory continuation of dual antiplatelet therapy
* Uncontrolled intercurrent illness that includes but is not limited to: uncontrolled infection, disseminated intravascular coagulation, psychiatric illness/compliance issues that would limit compliance with study protocol
* Any medical condition that in the opinion of the investigator places the participant at unacceptable risk for toxicity to investigational therapy