A Study of the Drug IMGN632 in Children With Leukemia That Has Come Back After Treatment or is Difficult to Treat

Inclusion Criteria:

* Patients from Children's Oncology Group (COG) sites must be enrolled on APAL2020SC
* Patients must be \>= 12 months and less than 22 years of age at the time of study enrollment
* Patient's weight at time of enrollment must be \>= 10 kg
* Patients must meet the eligibility in the appropriate Cohort for their diagnosis and disease status

  * Cohort 1 (Phase 1 Monotherapy):

    * Patients must meet all the following criteria:

      * Patient must have bone marrow sample showing \>= 5% leukemic blasts by flow cytometry
      * Patient must have been diagnosed with AML, B-ALL, T-ALL, or mixed phenotype acute leukemia (MPAL) meeting one of the following disease criteria:

        * Second or greater relapse OR
        * Disease that is refractory to relapse therapy

          * Refractory to relapse therapy is defined as persistent disease after at least one cycle of induction chemotherapy to treat the relapse disease
      * Patient must have leukemic blasts that are CD123-positive by flow cytometry as determined either by the treating institution or through reference laboratory testing.
  * Cohort 2 (Combination Dose Finding) and Cohort 3 (Randomized Phase 2 Combination):

    * Patients must meet all the following criteria:

      * Patient must have AML in first relapse with a bone marrow sample showing \>= 1% leukemic blasts by flow cytometry
      * Patient must have leukemic blasts that are CD123-positive by flow cytometry as determined either by the treating institution or through reference laboratory testing
      * For Cohort 3 only: Patient's AML is not treatment related
  * Central nervous system (CNS) disease - All Cohorts

    * Patients may have status of CNS1, CNS2, CNS3 disease without clinical signs or neurologic symptoms suggestive of CNS leukemia, such as facial nerve palsy, brain/eye involvement or hypothalamic syndrome
* Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1 or 2 (\>= 50% Lansky or Karnofsky score). Use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age. Patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score
* Patients must have fully recovered from the acute toxic effects of all prior anti-cancer therapy and must meet the following minimum duration from prior anti-cancer directed therapy prior to enrollment. Please refer to the table of myelosuppressive/Anticancer Agents on the COG website: https://www.cogmembers.org/uploadedFiles/Site/Disc/DVL/Documents/TableOfMyelosuppressiveAnti-CancerAgents.pdf. For agents not listed, the duration of this interval must be discussed with the study chair and the study-assigned Research Coordinator prior to enrollment.

  * Cytotoxic chemotherapy: Must not have received within 14 days of entry onto this study, except for hydroxyurea or corticosteroids

    * NOTE: Cytoreduction with hydroxyurea or corticosteroids must be discontinued prior to the start of protocol therapy. Use of steroids for other purposes such as premedication to prevent allergic reaction or during anesthesia is allowed
  * Intrathecal cytotoxic therapy

    * No waiting period is required for patients having received any combination of intrathecal cytarabine, methotrexate, and/or hydrocortisone
  * Antibodies: \>= 21 days must have elapsed from infusion of last dose of an antibody-drug conjugate. For unmodified antibodies or T cell engaging antibodies, 2 half-lives must have elapsed before enrollment. Any toxicity related to prior antibody therapy must be recovered to Grade =\< 1
  * Interleukins, interferons and cytokines (other than hematopoietic growth factors): \>= 21 days after the completion of interleukins, interferon or cytokines (other than hematopoietic growth factors)
  * Hematopoietic growth factors: \>= 14 days after the last dose of a long-acting growth factor (e.g., pegfilgrastim) or 7 days for short acting growth factor
  * Radiation therapy (RT):

    * 14 days have elapsed for local palliative RT (small port);
    * \>= 84 days must have elapsed if prior craniospinal RT or if \>= 50% radiation of pelvis;
    * \>= 42 days must have elapsed if other substantial bone marrow (BM) radiation
    * For combination therapy arms: Patients must have received =\< 13.6 Gy prior radiation to the mediastinum
  * Stem cell infusions:

    * \>= 84 days since allogeneic (non-autologous) bone marrow or stem cell transplant (with or without total body irradiation \[TBI\]) or boost infusion (any stem cell product; not including donor lymphocyte infusion \[DLI\])
    * No evidence of graft versus host disease (GVHD)
    * Patients must be off medications to treat or prevent either graft-versus-host disease post bone marrow transplant or organ rejection post-transplant for at least 14 days prior to start of protocol treatment
  * Cellular therapy: \>= 42 days after the completion of DLI (donor lymphocyte infusion) or any type of cellular therapy (e.g., modified T cells, natural killer \[NK\] cells, dendritic cells, etc.)
* Ejection fraction (EF) of \>= 55% or if EF unavailable, shortening fraction (SF) \>= 28% by echocardiogram (within 21 days prior to enrollment and start of protocol therapy \[repeat if necessary\]) AND
* Corrected QTc interval \< 500 msec (within 7 days prior to enrollment)
* Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 or a serum creatinine based on age/gender as follows (within 7 days prior to enrollment):

  * 1 to \< 2 years (age); 0.6 mg/dL (male) 0.6 mg/dL (female)
  * 2 to \< 6 years (age); 0.8 mg/dL (male) 0.8 mg/dL (female)
  * 6 to \< 10 years (age); 1 mg/dL (male) 1 mg/dL (female)
  * 10 to \< 13 years (age); 1.2 mg/dL (male) 1.2 mg/dL (female)
  * 13 to \< 16 years (age); 1.5 mg/dL (male) 1.4 mg/dL (female)
  * \>= 16 years (age); 1.7 mg/dL (male) 1.4 mg/dL (female)
* Direct bilirubin \< 2 mg/dL (\< 34 umol/L), (within 7 days prior to enrollment) AND
* Serum glutamate pyruvate transaminase SGPT (alanine aminotransferase \[ALT\]) =\< 135 U/L (within 7 days prior to enrollment)

  * If liver abnormality is due to leukemia infiltrate, the patient will remain eligible

Exclusion Criteria:

* Plans to administer any type of non-protocol prescribed anti-cancer therapy while on protocol directed therapy. For Cohort 1, additional intrathecal therapy is allowed per treating physician's discretion
* Strong inducers or inhibitors of CYP2D6 or CYP3A4 are prohibited for 7 days prior to the 1st dose of IMGN632 to the end of the treatment for both the Phase 1 Monotherapy Dose Finding and pharmacokinetic (PK) and the Combination Dose Finding components of the study. For patients not enrolled in a dose finding portion of the study, concomitant therapy with strong inducers or inhibitors of CYP2D6 or CYP3A4 is STRONGLY discouraged but not prohibited if clinically indicated
* Patients with acute promyelocytic leukemia (APL) or juvenile myelomonocytic leukemia (JMML)
* Patients with Down syndrome
* Patients with isolated extramedullary disease or those with minimal bone marrow disease not meeting the definition of relapsed or relapse refractory as defined above
* Patients with a prior history of Grade 4 VOD/SOS (veno-occlusive disease/sinusoidal obstructive syndrome) or any history of Grade 3 VOD/SOS that, at the discretion of the treating physician, places the patient at unacceptably high risk for future severe VOD/SOS
* Patients who are currently receiving another investigational drug
* Patients receiving medications for treatment of left ventricular systolic dysfunction
* Patients with Fanconi anemia, Kostmann syndrome, Shwachman syndrome or any other known congenital bone marrow failure syndrome
* Patients with known prior allergy to any of the medications used in protocol therapy
* Patients with documented active, uncontrolled infection at the time of study entry
* Patients with history of Wilson's disease or other copper-related disorder
* Pregnancy and breastfeeding:

  * Female patients who are pregnant since fetal toxicities and teratogenic effects have been noted for several of the study drugs. A pregnancy test is required for female patients of childbearing potential
  * Lactating females who plan to breastfeed their infants
  * Sexually active patients of reproductive potential (male and female) who have not agreed to use an effective contraceptive method or abstinence for the duration of their study participation and for 12 weeks after the last dose of IMGN632 or 6 months after last dose of DAUNOrubicin and cytarabine liposome, whichever is longer
* Regulatory requirements

  * All patients and/or their parents or legal guardians must sign a written informed consent
  * All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met