Inclusion Criteria:

- Must meet 1 of the following criteria:

- Histologically or cytologically confirmed solid tumors (dose-escalation only)

- Locally advanced, inoperable, or metastatic disease

- Evaluable or measurable disease

- Diagnosis of acute myeloid leukemia (AML) for which no other standard therapy,
including stem cell transplantation, is expected to result in meaningful
clinical response (expansion cohort only)

- Refractory or relapsed disease

- Chronic myelogenous leukemia in blast crisis allowed

- No acute promyelocytic leukemia with t(15;17)

- Must consent to have fresh tumor, bone marrow aspirate, and biopsy obtained

- No untreated, symptomatic, or unstable brain metastases

- No active CNS involvement for patients with AML

- ECOG performance status 0-1

- ANC ≥ 1,500/mm³ (dose-escalation only)

- Platelet count ≥ 100,000/mm³ (dose-escalation only)

- Hemoglobin ≥ 10 g/dL (dose-escalation only)

- Total bilirubin ≤ 1.5 times upper limit of normal (ULN)

- ALT and AST ≤ 3 times ULN (≤ 5 times ULN for liver metastasis)

- Creatinine clearance ≥ 40 mL/min

- Albumin > 3.0 g/dL

- Plasma phosphorus > lower limit of normal (with supplementation)

- INR ≤ 1.5

- APTT ≤ 1.5 times ULN (if not on anticoagulants)

- Able to swallow oral medications

- ≥ 16 years old (expanded cohort patients recruited at the University of Colorado
site)

- Must have tolerated prior sorafenib tosylate (dose: 400 mg twice daily), if
applicable

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective double-barrier contraception during the study and
for 90 days after completion of study therapy

- No history of cardiac disease, including any of the following:

- NYHA class II-IV congestive heart failure

- Active coronary artery disease

- Prior diagnosis of bradycardia or other cardiac arrhythmia defined as ≥ grade 2
or uncontrolled hypertension

- Myocardial infarction (MI) within the past 6 months

- Persistent tachycardia

- LVEF < 40% by MUGA

- Second- or third-degree heart block

- QTc > 490 msec

- ST-T wave changes consistent with acute MI or acute ischemia

- No clinically active serious infections defined as ≥ grade 2

- No substance abuse, medical, psychological, or social conditions that may, in the
opinion of the Investigator, interfere with the patient's participation or evaluation
of the study results

- No condition that is unstable or that could jeopardize the safety of the patient and
his/her study compliance

- No known HIV infection

- No significant gastrointestinal disorder that, in the opinion of the Investigator,
could interfere with the absorption of entinostat and/or sorafenib tosylate including
any of the following:

- Significant, uncontrolled inflammatory bowel disease

- Abdominal fistula or gastrointestinal perforation within the past 6 months

- Extensive small bowel resection

- Requiring tube feeding or parenteral hydration and/or nutrition

- No concurrent immunosuppressive therapies, including high-dose systemic
corticosteroids (> 0.5 mg/kg/day prednisone or equivalent) unless used intermittently
or as a tapered course for ≤ 4 weeks

- Concurrent hydroxyurea and/or anagrelide allowed

- Concurrent warfarin allowed provided the dose has been stable for the past 2 months
and INR has been between 2 and 3

- More than 4 weeks since prior chemotherapy, immunotherapy, or investigational agents
(=< 2 weeks for leukemia patients in expansion cohort)

- More than 2 weeks since prior palliative radiotherapy

- More than 4 weeks since major surgery

- More than 2 weeks since minor surgery (e.g., talc pleurodesis, excisional biopsy,
etc.)

- Concurrent hormonal therapies (e.g., LHRH antagonists, megestrol, octreotide,
calcitonin, etc.) allowed

- No concurrent strong CYP3A4 inducers or inhibitors, including, but not limited to,
any of the following:

- Valproic acid

- Rifampin

- Phenobarbital

- Phenytoin

- Carbamazepine

- Ketoconazole

- Erythromycin

- Grapefruit

- No other concurrent anticancer therapy including chemotherapy, radiotherapy
(including palliative), or immunotherapy (except hydroxyurea in leukemia patients
during course 1)

- No other concurrent investigational agents