Inclusion Criteria:

        For Part 1:Patients must have one of the following diagnoses based on World Heath
        Organization (WHO) diagnostic criteria:

          -  Aggressive systemic mastocytosis (ASM).

          -  Systemic mastocytosis with an associated hematologic neoplasm (SM-AHN) and at least 1
             C-finding attributable to systemic mastocytosis (SM). The AHN must be myeloid, with
             the following exceptions that are excluded: Acute myeloid leukemia (AML),
             Myelodysplastic syndrome (MDS) that is very high- or high-risk as defined by the
             International prognostic scoring system for myelodysplastic syndromes (IPSS-R) and
             Philadelphia chromosome positive malignancies.

          -  Mast cell leukemia (MCL).

          -  Histologically- or cytologically- confirmed myeloid malignancy that is relapsed or
             refractory to standard treatments. AML, MDS that is very high- or high-risk as defined
             by the IPSS-R, and Philadelphia chromosome positive malignancies are excluded.

          -  Upon discussion with the sponsor, other relapsed or refractory, potentially
             avapritinib-responsive hematologic neoplasms (e.g., evidence of aberrant KIT or
             platelet derived growth factor receptor (PDGFR) signaling) may be considered for
             enrollment.

        For Part 2, patients must have one of the following diagnoses, based on WHO diagnostic
        criteria:

          -  ASM.

          -  SM-AHN. The AHN must be myeloid, with the following exceptions that are excluded: AML,
             MDS that is very high- or high-risk as defined by the IPSS-R, and Philadelphia
             chromosome positive malignancies.

          -  MCL.

        For Part 2, Cohort 2, patients must have at least 1 measurable C-finding per modified
        IWG-MRT-ECNM criteria at Baseline, attributed to SM unless diagnosis is MCL, which does not
        require a C-finding.

          -  Cytopenias: ANC < 1.0 × 10⁹/L or hemoglobin < 10 g/dL or platelet count < 75 × 10⁹/L.

          -  Symptomatic ascites or pleural effusion requiring medical intervention such as: use of
             diuretics (Grade 2) or ≥ 2 therapeutic paracenteses or thoracenteses (Grade 3) at
             least 28 days apart over the 12 weeks before study entry and 1 of the procedures is
             performed during the 6 weeks before study start (C1D1).

          -  ≥ Grade 2 abnormalities in direct bilirubin (> 1.5 × upper limit of normal [ULN]),
             aspartate aminotransferase (AST; > 3.0 × ULN), alanine aminotransferase (ALT; > 3.0 ×
             ULN), or alkaline phosphatase (> 2.5 × ULN) with 1 of the following present: ascites
             or clinically relevant portal hypertension or liver mast cell infiltration that is
             biopsy-proven or no other identified cause of abnormal liver function.

          -  ≥ Grade 2 hypoalbuminemia (< 3.0 g/dL).

          -  A spleen that is palpable ≥ 5 cm below the left costal margin.

          -  Transfusion-dependent anemia defined as: transfusion of ≥ 6 units packed red blood
             cells (PRBCs) in the 12 weeks before start of treatment (C1D1) and most recent
             transfusion occurring during the preceding 4 weeks and transfusion administered for
             hemoglobin ≤ 8.5 g/dL and reason for transfusion is not bleeding, hemolysis, or
             therapy-related.

        Eastern Cooperative Oncology Group (ECOG) performance status of 0-3.

        Exclusion Criteria:

          -  QT interval corrected using Fridericia's formula (QTcF) >480 milliseconds

          -  Platelet count <50,000/μL (within 4 weeks of the first dose of study drug) or
             receiving platelet transfusion(s)

          -  Absolute neutrophil count <500/μL

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) >3 x the upper
             limit of normal (ULN); >5 × ULN if associated with clinically suspected liver
             infiltration by mastocytosis or another disease for which the patient enrolled into
             the study

          -  Total bilirubin >1.5 × ULN; >3 × ULN if associated with liver infiltration by the
             disease being treated or in the presence of Gilbert's Disease (In the case of
             Gilbert's disease, a direct bilirubin > 2.0 ULN would be an exclusion.)

          -  Estimated (Cockroft-Gault formula) or measured creatinine clearance <40 mL/min

          -  Brain malignancy or metastases to the brain

          -  History of a seizure disorder or requirement for anti-seizure medication

          -  Known risk of intracranial bleeding, such as a brain aneurysm or history of subdural
             or subarachnoid bleeding

          -  Eosinophilia and known positivity for the FIP1L1-PGDFRA fusion, unless the patient has
             demonstrated relapse or progressive disease on prior imatinib therapy