Inclusion Criteria

DISEASE CHARACTERISTICS:

- Histologically confirmed diagnosis of one of the following:

- Relapsed or refractory extracranial solid tumor

- Relapsed or refractory leukemia

- At least 25% blasts in the bone marrow (M3) with the exception of patients
with acute myeloid leukemia (AML), who must have > 20% blasts in the bone
marrow

- Relapsed or refractory myeloproliferative neoplasm (MPN)

- At original diagnosis or relapse

- Current diagnostic criteria for MPNs include polycythemia vera, essential
thrombocythemia, juvenile myelomonocytic leukemia, myelofibrosis, and
atypical chronic myeloid leukemia

- Relapsed or refractory leukemia or MPN that have confirmed JAK mutations and/or
positive TSLPR surface staining

- Testing for JAK mutations and/or confirmed positive flow cytometry surface
staining for the thymic stromal lymphopoietin receptor (TSLPR; encoded by
CRLF2) must be performed by a CLIA-approved laboratory

- Measurable or evaluable disease (for patients with solid tumors)

- Current disease state is one for which there is no known curative therapy or therapy
proven to prolong survival with an acceptable quality of life

- No known active CNS involvement (radiographic or cytologic)

PATIENT CHARACTERISTICS:

- Karnofsky performance status (PS) 50-100% (for patients > 16 years old) or Lansky PS
50-100% (for patients ≤ 16 years old)

- Patients who are unable to walk because of paralysis, but who can actively sit
up in a wheelchair, will be considered ambulatory for the purpose of assessing
the performance status

- Patients with solid tumors* must meet the following criteria:

- Peripheral ANC ≥ 1,000/mm^3

- Platelet count ≥ 100,000/mm^3 (transfusion-independent, defined as > 7 days
since prior platelet transfusions)

- Hemoglobin ≥ 8.0 g/dL (may receive RBC transfusions)

- Not refractory to to red cell or platelet transfusion

- ALT ≤ 110 U/L NOTE: *Patients with solid tumors and known bone marrow metastatic
disease are eligible for study, but not evaluable for hematologic toxicity.
These patients must not be known to be refractory to RBC or platelet
transfusions.

- Patients with leukemia or MPNs must meet the following criteria:

- Platelet count ≥ 20,000/mm^3 (may receive platelet infusions)

- Hemoglobin ≥ 8.0 g/dL (may receive RBC transfusions)

- ALT ≤ 225 U/L

- Creatinine clearance or radioisotope GFR ≥ 70 mL/min OR serum creatinine based on
age/gender as follows:

- ≤ 0.6 mg/dL (for patients 1 to < 2 years old)

- ≤ 0.8 mg/dL (for patients 2 to < 6 years old)

- ≤ 1 mg/dL (for patients 6 to < 10 years old)

- ≤ 1.2 mg/dL (for patients 10 to < 13 years old)

- ≤ 1.4 mg/dL (for female patients ≥ 13 years old)

- ≤ 1.5 mg/dL (for male patients 13 to < 16 years old)

- ≤ 1.7 mg/dL (for male patients ≥ 16 years old)

- Bilirubin (sum of conjugated + unconjugated) ≤ 1.5 times upper limit of normal for
age

- Serum albumin ≥ 2 g/dL

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception

- Able to swallow crushed or whole tablets

- Nasogastric or G tube administration is not allowed

- Body surface area ≥ 0.65 m^2 (for patients at dose level -1, 1, and 2)

- No uncontrolled infection, including patients with known active HIV or chronic
hepatitis

- No patients who, in the opinion of the investigator, may not be able to comply with
the safety monitoring requirements of the study

PRIOR CONCURRENT THERAPY:

- Fully recovered from the acute toxic effects of all prior anticancer therapy

- At least 2 weeks since prior local palliative radiotherapy (small port)

- At least 6 months since prior total-body irradiation (TBI), craniospinal
radiotherapy, or radiotherapy to ≥ 50% of the pelvis (for patients with solid tumors)

- At least 3 months since prior TBI, craniospinal radiotherapy, or radiotherapy to ≥
50% of the pelvis (for patients with leukemia)

- At least 3 months since prior stem cell transplantation or rescue without TBI and no
evidence of active graft-vs-host disease

- At least 6 weeks since other substantial bone marrow radiation

- At least 3 weeks since prior myelosuppressive therapy (6 weeks for nitrosourea) (for
patients with solid tumors)

- At least 2 weeks since prior cytoxic chemotherapy (for patients with leukemia or
MPNs)

- Hydroxyurea may be initiated and continued for up to 24 hours before the start
of study treatment

- Intrathecal cytarabine (Ara-C) is not myelosuppressive chemotherapy

- Patients with leukemia are permitted to receive intrathecal chemotherapy,
including methotrexate or cytarabine, only if this is given at the time of
diagnostic lumbar puncture at least 24 hours prior to the start of INCB018424

- At least 2 weeks since prior long-acting hematopoietic growth factor (e.g., Neulasta)
or 1 week for a short-acting growth factor

- For agents that have known adverse events occurring beyond 1 week, this period
must be extended beyond the time during which adverse events are known to occur
(as discussed with the study chair)

- At least 1 week since prior therapy with a biologic (antineoplastic) agent

- For agents that have known adverse events occurring beyond 1 week, this period
must be extended beyond the time during which adverse events are known to occur
(as discussed with the study chair)

- At least 3 half-lives of antibody since prior monoclonal antibody

- No other concurrent investigational drugs

- No other concurrent anticancer agents, including chemotherapy, radiotherapy,
immunotherapy, or biologic therapy

- No concurrent systemic steroids (i.e., prednisone > 10 mg)

- No concurrent aspirin > 150 mg/day

- No concurrent medications for myelofibrosis (e.g., hydroxyurea, interferon,
thalidomide, busulfan, lenalidomide, or anagrelide)

- No concurrent cyclosporine, tacrolimus, or other agents to prevent graft-vs-host
disease after bone marrow transplant or organ rejection after transplant