Entinostat and Sorafenib Tosylate in Treating Patients With Advanced or Metastatic Solid Tumors or Refractory or Relapsed Acute Myeloid Leukemia

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