A Trial of Oral 5-azacitidine in Combination With Romidepsin in Advanced Solid Tumors, With an Expansion Cohort in Virally Mediated Cancers and Liposarcoma

Inclusion Criteria: * Understand and voluntarily sign informed consent form (ICF). * Age ≥ 18 years at time of signing ICF. * Adhere to study visit schedule and other protocol requirements. * Histologically or cytologically confirmed metastatic or unresectable solid tumor (phase I dose escalation), OR HPV+ nasopharyngeal cancer, HPV+ cervical cancer or liposarcoma (for expansion cohort). * Failed at least one previous chemotherapy regimen for metastatic disease if standard therapies exist. * Measurable disease per RECIST 1.1 * Life expectancy ≥ 12 weeks * No previous cancer therapy ≥ 4 weeks. * ECOG performance status ≤ 1 * Laboratory test results: * Absolute neutrophil count ≥ 1500/mm³ * Platelet ≥ 100,000/mm³ * Serum creatinine levels \< 1.5 X ULN OR creatinine clearance \>60 mL/min/1.73 m2 for subjects with creatinine levels \> institutional normal * Serum bilirubin ≤ 1.5 times the upper limit of the normal range for the laboratory (ULN). * AST (SGOT) and ALT (SGPT) ≤ to 2.5 x ULN * Disease free of prior malignancies ≥ 5 years (except currently treated basal cell, squamous cell carcinoma of the skin, or carcinoma in situ of the cervix or breast). * Women of childbearing potential should be advised to avoid becoming pregnant and men should be advised to not father a child while receiving treatment with 5-azacitidine. All men/women of childbearing potential must use acceptable methods of birth control throughout the study. Exclusion Criteria: * Serious medical conditions, laboratory abnormality, or psychiatric illness that would prevent the subject from signing ICF. * Pregnant or breastfeeding women. (Lactating women must agree not to breast feed while taking 5-azacitidine). * Conditions, including laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret study data. * Chemotherapy, radiotherapy, or experimental drug or therapy ≤ 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to enrollment or adverse events \< grade 1 due to agents administered \>4 weeks earlier except for stable grade 2 neuropathy. * No other concomitant investigational agents. * Known or suspected hypersensitivity to 5-azacitidine, romidepsin, mannitol or other agents used in this study. * Uncontrolled brain metastases. * Known positive for HIV, infectious hepatitis, type B or C. * Uncontrolled intercurrent illness * Known GI disorders precluding oral administration of 5-azacitidine. * Known cardiac abnormalities such as: * Congenital long QT syndrome * QTc interval ≥ 500 milliseconds; * Myocardial infarction ≤6 months of C1D1. Subjects with a history of myocardial infarction between 6-12 months prior to C1D1 who are asymptomatic and have had a negative cardiac risk assessment (treadmill stress test, nuclear medicine stress test, or stress echocardiogram) since the event may participate; * Other significant ECG abnormalities including 2nd degree atrio-ventricular (AV) block type II, 3rd degree AV block, or bradycardia (ventricular rate less than 50 beats/min); * Symptomatic coronary artery disease (CAD), e.g., angina. In any patient in whom there is doubt, the patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present; * Screening ECG showing evidence of cardiac ischemia (ST depression, depression of ≥2 mm, measured from isoelectric line to the ST segment). If in any doubt, patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present; * Congestive heart failure (CHF) that meets New York Heart Association (NYHA) Class II to IV definitions and/or ejection fraction \<40% by MUGA scan or \<50% by echocardiogram and/or MRI; * Known history of sustained ventricular tachycardia (VT), ventricular fibrillation (VF), Torsade de Pointes, or cardiac arrest unless currently addressed with an automatic implantable cardioverter defibrillator (AICD); * Hypertrophic cardiomegaly or restrictive cardiomyopathy; * Uncontrolled hypertension, i.e., blood pressure (BP) of ≥160/95; patients who have a history of hypertension controlled by medication must be on a stable dose (for at least one month) and meet all other inclusion criteria; or * Cardiac arrhythmia requiring an anti-arrhythmic medication (excluding stable doses of beta-blockers) * Patients taking drugs leading to significant QT prolongation * Concomitant use of CYP3A4 inhibitors