Brief Summary: This phase I trial studies the best dose and side effects of flotetuzumab for the treatment of patients with blood cancers (hematological malignancies) that have spread to other places in the body (advanced) and have come back after a period of improvement (relapsed) or does not respond to treatment (refractory). Flotetuzumab is a monoclonal antibody that may interfere with the ability of cancer cells to grow and spread.

Detailed Description: PRIMARY OBJECTIVES: I. To determine the maximum tolerated dose (recommended phase 2 dose, RP2D) of flotetuzumab, when given as a single agent. II. Evaluate the safety and tolerability of flotetuzumab in CD123-positive advanced acute lymphoblastic leukemia (ALL) (Cohort A) and other hematological malignancies (Cohort B), by evaluation of toxicities including: type, frequency, severity, attribution, and duration of the toxicity. SECONDARY OBJECTIVES: I. Obtain preliminary estimates of remission; (complete remission \[CR\], complete remission with incomplete count recovery \[CRi\], complete remission with partial hematological recovery \[CRh\] or morphologic leukemia free state \[MLFS\] in Cohort A or CR/molecular response \[MR\] in Cohort B) rate and duration. II. Estimate 1-year overall survival. III. Evaluate minimal residual disease (MRD) status in responders in the ALL cohort. IV. Evaluate the percentage of patients who receive subsequent allogeneic transplantation. EXPLORATORY OBJECTIVES: I. Examine immune profile pre- and post-treatment with flotetuzumab. II. Assess the association between CD123 expression and tumor response. III. Assess the association between alterations in tumor genetic or microenvironment with response. IV. Assess cytokine levels during therapy. OUTLINE: This is a dose-escalation study. INDUCTION THERAPY: Patients receive flotetuzumab via continuous intravenous (IV) infusion on days 1-28. Patients who achieve stable disease (SD)/partial remission (PR) (Cohort A) or PR/clinical improvement (CI) (Cohort B), receive an additional induction cycle. Patients who achieve PR (Cohort A) or PR/CI/major molecular response (MMR) (Cohort B) after cycle 2 re-induction, may continue induction therapy for up to 4 more cycles. CONSOLIDATION THERAPY: Patients who achieve CR/CRi/CRh/MLFS (Cohort A) or CR/MR (Cohort B) after cycle 1 or cycle 2 of induction therapy, receive flotetuzumab via continuous IV infusion on days 1-28 for up to 5 and 6 cycles, respectively, in the absence of disease progression or unacceptable toxicity. Patients with PR (Cohort A) or PR/CI/MMR (Cohort B) who have received up to 6 cycles of induction therapy may receive up to 2 cycles of consolidation therapy in the absence of disease progression or unacceptable toxicity. SUPPORTIVE CARE: Patients also receive acetaminophen orally (PO) or ibuprofen PO every 8 hours for 48 hours, diphenhydramine or equivalent IV or PO every 8 hours for 48 hours, ranitidine or equivalent IV every 8 hours for 48 hours, and dexamethasone IV up to 30 minutes prior to dosing and then at 12 hours after dosing on week 1 days 1 and 7. After completion of study treatment, patients are followed up at 30 days, then every 3 months for 1 year.