Inclusion Criteria:

          -  Eligible patients will be aged >= 18 years. Pediatric patients age 2 years and older
             will be considered on a case by case basis.

          -  Diagnosis of blastic plasmacytoid dendritic cell neoplasm (BPDCN) according to World
             Health Organization (WHO) classification or confirmed by hematopathology

          -  The patients must be in partial response or better

          -  > 30 days post-transplant without active or chronic infections

          -  Karnofsky performance status >= 60%; Lansky >= 60

          -  Left ventricular ejection fraction (LVEF) >= institutional lower limit of normal by
             multigated acquisition (MUGA) scan or echocardiogram within 30 days of first protocol
             treatment

          -  Diffusion capacity of the lung for carbon monoxide (DLCO) > 40% of predicted value
             (corrected for hemoglobin) within 3 months of registration

          -  Forced expiratory volume in 1 second (FEV1) > 40% of predicted value within 3 months
             of registration

          -  Forced vital capacity (FVC) > 40% of predicted value within 3 months of registration

          -  Serum creatinine =< 1.5 mg/dL (133 mmol/L)

          -  Serum albumin >= 3.2 g/dL (or >= 32 g/L) without IV albumin within the previous 72
             hours

          -  Bilirubin =< 1.5 x the upper limit of normal ([ULN] except patients with Gilbert
             syndrome in whom bilirubin level of > 1.5 x ULN will be allowed)

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 times ULN

          -  Hemoglobin >= 8 g/dL with or without transfusion in the last 7 days

          -  Absolute neutrophil count (ANC) >= 1000 without granulocyte colony stimulating factor
             (GCSF) or granulocyte-macrophage colony-stimulating factor (GMCSF) in the last 2 weeks
             prior to screening

          -  Platelets >= 50,000micro/mL

          -  For allo-HCT, no >= grade 2 visceral (gut or liver) acute graft versus host disease
             (GVHD) and no >= grade 3 or any other acute GVHD (patients with chronic GVHD will be
             allowed at the discretion of the investigator)

          -  Patient agrees to use acceptable contraceptive methods for the duration of time in the
             study, and to continue to use acceptable contraceptive methods for 2 months after the
             last tagraxofusp infusion

          -  Woman of child bearing potential (WOCBP) with a negative serum or urine pregnancy test
             within 14 days of tagraxofusp treatment

          -  Patient or patient's legal representative, parent(s) or guardian able to sign informed
             consent

          -  The patient can adhere to the study visit schedule and other protocol requirements,
             including follow-up for survival assessment

        Exclusion Criteria:

          -  The patient has persistent clinically significant non-hematologic toxicities >= grade
             2 (excluding alopecia, nausea, and fatigue)

          -  Evidence of central nervous system (CNS) involvement

          -  Uncontrolled and active pulmonary disease

          -  Requirement for oxygen treatment

          -  Receiving chemotherapy, radiotherapy or other anti-cancer therapy within 14 days of
             first dose of study drug. There must be at least a 6-week interval from the last
             immunotherapy therapy

          -  Uncontrolled infection

          -  Human immunodeficiency virus (HIV)/hepatitis B and/or C

          -  Any history of invasive malignancy in the last 2 years excluding any malignancy such
             as cervical cancer or skin cancer (excluding melanoma) that is considered cured at the
             time of screening

          -  Pregnant or breast-feeding woman

          -  Patient has uncontrolled intercurrent illness or medical/psychiatric condition that
             would limit compliance with study requirements or that would in the investigator's
             opinion place the patient at an unacceptably high risk for toxicities

          -  Clinical significant cardiopulmonary disease including uncontrolled or New York Heart
             Association (NYHA) class 3 or 4 congestive heart failure, uncontrolled angina,
             uncontrolled hypertension, uncontrolled arrhythmia, myocardial infarction or stroke
             within 6 months of first protocol treatment or corrected QT (QTc) > 480 ms