Flotetuzumab in Treating Patients With Recurrent or Refractory CD123 Positive Blood Cancer

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative. * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval. * Eastern Cooperative Oncology Group (ECOG) =\< 2 * Histologically confirmed diagnosis of * Cohort A. Acute lymphoblastic leukemia * B-cell phenotype: patients with relapsed or refractory ALL who have received at least 2 prior regimens and failed or are ineligible for CD19-based target therapy * T-cell phenotype: patients with relapsed or refractory who have received at least 1 prior regimen * Cohort B. Other CD123+ hematological malignancies that failed standard regimens, excluding acute myeloid leukemia and myelodysplastic syndrome * Blastic plasmacytoid dendritic cell neoplasm (BPDCN) patients who have failed or relapsed after initial therapy * Chronic myeloid leukemia (CML) patients who have failed or relapsed or ineligible for third generation tyrosine kinase inhibitor (ponatinib) * Hairy cell leukemia patients who have failed or progressed shortly after purine analogs or failed 2 cycles of purine analog * Systemic mastocytosis patients who have failed or progressed on midostaurin * Hodgkin lymphoma patients who have failed or relapsed after PD-1/PD-L1- inhibitors and brentuximab…