Entinostat Neuroendocrine (NE) Tumor

Inclusion Criteria: 1. Pathologically confirmed stage intravenous (IV) unresectable relapsed, or unresectable refractory abdominal neuroendocrine tumor from the last biopsy available which may be the initial diagnostic biopsy. Relapsed disease is defined as progressive disease following systematic therapy with lanreotide or equivalent and either Sunitinib or everolimus or both. Refractory disease is defined as disease not responding to or having progressed within 1 month of the last dose of most recent systemic therapy to include lanreotide or an analog and either sunitinib or everolimus. (Note, small cell carcinoma and large cell undifferentiated neuroendocrine tumors will be excluded from this trial). 2. Eligibility for stage 2 of the study, if the extension stage is opened, will be determined by ribonucleic acid-sequencing (RNA-seq) analysis and master regulator profile of a single fresh needle biopsy specimen obtained during study screening. 3. Documented disease that is radiographically measurable. 4. Last dose of prior therapy must be \> 21 days before the first dose of study drug administration. There is no upper limit to number of prior therapies. However, the patient must have recovered from acute toxicities from the most recent therapy to grade 1 or less. 5. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 (must be done within 7 days prior to study drug administration). 6. Age 18 years or older 7. Total Bilirubin ≤ 1.5 x Upper Limit of Normal (ULN) and aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 2.5 x ULN (results within 7 days before study drug administration), ≤5×ULN for patients with liver metastases. 8. Serum creatinine ≤ 1.5 x ULN (results within 7 days before study drug administration) 9. Absolute neutrophil counts of ≥ 1500/μL (without growth factor support), platelet counts ≥100,000/μL (without transfusion support); and hemoglobin ≥9 g/dL results within 7 days before study drug administration. 10. Patients or their legal representative must be able to read, understand, and sign a written informed consent 11. International Normalized Ratio (INR) or Prothrombin Time (PT) ≤1.5×ULN unless patient is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants and activated partial Thromboplastin Time (aPTT) ≤1.5×ULN unless patient is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants 12. If a female of childbearing potential, has a negative serum blood pregnancy test during screening and a negative urine pregnancy test within 3 days prior to receiving the first dose of study drug. If the screening serum test is done within 3 days prior to receiving the first dose of study drug, a urine test is not required. Note: Women of childbearing potential (WoCP) are any women between menarche and menopause who have not been permanently or surgically sterilized and are capable of procreation. Permanent sterilization includes hysterectomy and/or bilateral oophorectomy and/or bilateral salpingectomy but excludes bilateral tubal occlusion. WoCP include non-women who have experienced menopause onset \< 12 months prior to enrollment. 13. If a female of childbearing potential, willing to use 2 methods of birth control or willing to abstain from heterosexual activity for the course of the study through 120 days after the last dose of study drug. 14. If male, agrees to use an adequate method of contraception starting with the first dose of study drug through 120 days after the last dose of study drug. Exclusion Criteria: Patients fulfilling any of the following criteria will not be admitted into the study: 1. Patients with another active cancer (excluding basal cell carcinoma or cervical intraepithelial neoplasia (Cervical Intraepithelial Neoplasia (CIN) / cervical carcinoma in situ) or melanoma in situ)). Prior history of other cancer is allowed, as long as there is no active disease within the prior 5 years. 2. Pregnant or lactating women. Women of child-bearing potential (WOCBP) must have a negative serum pregnancy test documented within 3 days prior to start of study drug. 3. Patients with uncontrolled intercurrent illness, active or uncontrolled infections, or a fever \>38.5°C that has not been evaluated for infection up to the day of initial dosing. Patients with documented history of tumor fever are accepted provided acute or chronic infection has been excluded as possible cause of the fever. 4. Patients who have been treated with any investigational drug within 28 days prior to the first dose of study medication, or who are receiving concurrent treatment with other experimental drugs or anti-cancer therapy. 5. Prior treatment with histone deacetylase (HDAC) inhibitors (e.g. valproic acid, Zolinza® (SAHA), romidepsin (Istodax®). 6. History of pericarditis or pericardial effusion that had required medical or surgical intervention in the last 6 months, or myocardial infarction or arterial thromboembolic events within 6 months, or experiencing severe or unstable angina, or New York Heart Association (NYHA) Class III or IV disease, or a corrected QT (QTc) interval \>0.47 seconds 7. Known human immunodeficiency virus (HIV) or a history of active Hepatitis B or C as evidenced by laboratory abnormalities in addition to positive serology. Testing is not required for patients not suspected of having these conditions 8. Any condition (e.g., known or suspected poor compliance, psychological instability, geographical location, etc) that, in the judgment of the investigator, may affect the patient's ability to sign the informed consent and comply with study procedures 9. Any condition that will put the patient at undue risk or discomfort as a result of adherence to study procedures 10. Presence or history of brain metastases. 11. Uncontrolled hypertension or diabetes mellitus 12. Any contraindication to oral agents or significant nausea and vomiting, malabsorption, or significant small bowel resection that, in the opinion of the investigator, would preclude adequate absorption. 13. Allergy to benzamide or inactive components of entinostat. 14. Patients may not be taking any corticosteroid for any reason while on study and all corticosteroids must be stopped two weeks prior to initiation of study drug.