Abbreviated Inclusion Criteria:

        All Patients (Stages 2 and 3A):

          1. The patient is ≥18 years old.

          2. The patient has a life expectancy of >6 months.

          3. The patient has an Eastern Cooperative Oncology Group (ECOG) performance status (PS)
             of 0-2.

          4. The patient has adequate baseline organ function, including cardiac, renal, and
             hepatic function:

               -  Left ventricular ejection fraction (LVEF) ≥ institutional lower limit of normal
                  as measured by multigated acquisition scan (MUGA) or 2-dimensional (2-D)
                  echocardiogram (ECHO) within 28 days prior to start of therapy and no clinically
                  significant abnormalities on a 12-lead electrocardiogram (ECG)

               -  Serum creatinine ≤1.5 mg/dL

               -  Serum albumin ≥3.2 g/dL (or ≥32 g/L) in the absence of receipt of (IV) albumin
                  within the previous 72 hours

               -  Bilirubin ≤1.5 mg/dL

               -  Aspartate transaminase (AST) and alanine transaminase (ALT) ≤2.5 times the upper
                  limit of normal (ULN)

               -  Creatine phosphokinase (CPK) ≤2.5 times the ULN

               -  Absolute neutrophil count (ANC) ≥0.5 × 10⁹/L

        Additional Abbreviated Inclusion Criteria Specific to Patients with MF (Stage 2):

          1. Patient meets the 2016 WHO diagnostic criteria for MF and has an IPSS/DIPSS/DIPSS-plus
             intermediate-2 or high-risk disease. Patients with IPSS/DIPSS/DIPSS-plus low or
             intermediate-1 risk disease who have at least one of the following symptoms are also
             eligible: MF-related anemia (Hb <10 g/dL), splenomegaly (palpable size >10 cm),
             leukocytosis (WBC >25 × 10⁹/L), marked thrombocytosis (platelet count >1000 × 10⁹/L),
             or constitutional symptoms (weight loss >10%, during prior 6 months or fever [>37.5ºC
             or drenching night sweats for >6 weeks]), as recommended by the ELN/IWG 2018 criteria.

          2. Patient is approved JAK therapy (JAK1/JAK2 or JAK2) resistant/refractory or
             intolerant, in accordance with the ELN/IWG 2018 criteria, and at least 4 weeks have
             elapsed between the last dose of any MF-directed drug treatments; excluding HU, and
             study enrollment (first dose). HU can be continued until 2 weeks prior to study
             enrollment.

          3. Patient is not eligible for an immediate allo-SCT.

        Additional Abbreviated Inclusion Criteria Specific to Patients with CMML (Stage 3A):

          1. Patient has a 2016 WHO-defined diagnosis of CMML (persistent monocytosis ≥1 × 10⁹/L
             for at least 3 months, with other causes excluded, and monocytes ≥10% of WBC in
             peripheral blood, no criteria and no previous history of CML, ET, PV, and acute
             promyelocytic leukemia; if eosinophilic, neither PDGFRA, PDGFRB, FGFR1 rearrangements
             nor PCM1-JAK2 translocation; <20% blasts in peripheral blood and bone marrow aspirate;
             >1 following criteria - dysplasia in >1 myeloid lineage, acquired clonal cytogenetic
             or molecular abnormality in hematopoietic cells).

          2. Patient has 2016 WHO-defined CMML-1 (2-4% blasts in peripheral blood and/or 5-9%
             blasts in bone marrow) and CMML-2 (5-19% blasts in peripheral blood and/or 10-19%
             blasts in bone marrow, and/or presence of Auer rods).

          3. Patient is refractory/resistant/intolerant to HMAs, or HU, or intensive chemotherapy
             OR patient is classified as high-risk based on the presence of morphological features,
             as described by the 2016 WHO prognostic system, and the clinical and molecular
             features described in molecularly-integrated prognostic systems, such as the GFM, MMM,
             and the CMML specific prognostic model (CPSS-Mol), and thus is not expected to benefit
             from HMAs.

          4. Patient is ineligible for an immediate allo-SCT.

        Abbreviated Exclusion Criteria:

        All Patients (Stages 2 and 3A):

          1. Persistent clinically significant toxicities Grade ≥2 from previous therapies not
             readily controlled by supportive measures (excluding alopecia, nausea, and fatigue).

          2. Treatment with any disease-related therapy, including radiation therapy or
             investigational agent, within 14 days of study entry.

          3. Allogeneic SCT within 3 months of study entry.

          4. Previous treatment with tagraxofusp or known hypersensitivity to any components of the
             drug product.

          5. Active malignancy and/or cancer history (excluding myeloproliferative disorders and
             concomitant myeloid malignancies as specified in the inclusion criteria) that can
             confound the assessment of the study endpoints. Patients with a past cancer history
             (within 2 years of entry) and/or ongoing active malignancy or substantial potential
             for recurrence must be discussed with the Sponsor before study entry. Patients with
             the following neoplastic diagnoses are eligible: non-melanoma skin cancer, carcinoma
             in situ (including superficial bladder cancer), cervical intraepithelial neoplasia, or
             organ-confined prostate cancer with no evidence of progressive disease.

          6. Clinically significant cardiovascular disease, pulmonary disease, or known active or
             suspected disease involvement of the central nervous system (CNS).

          7. Receiving immunosuppressive therapy, with the exception of corticosteroids as
             specified in the inclusion criteria and tacrolimus, for treatment or prophylaxis of
             graft-versus-host disease (GVHD).

          8. Uncontrolled intercurrent illness.

          9. Patient is pregnant or breast feeding.

         10. Patient has known human immunodeficiency virus (HIV), Hepatitis B or Hepatitis C.

         11. Patient is oxygen-dependent.

        Additional Exclusion Criteria Specific to Patients with MF and CMML (Stages 2 and 3A)
        apply.