A Phase 1/2 Study of PXD101 (Belinostat) in Combination With Cisplatin, Doxorubicin and Cyclophosphamide in the First Line Treatment of Advanced or Recurrent Thymic, Malignancies

-INCLUSION CRITERIA: 1. Both the phase I and phase II portions of the protocol will be only open to patients with histologically confirmed advanced stage (Masaoka stage III or IV) thymic malignancies. 2. Patients must be chemotherapy na(SqrRoot) ve for the treatment of advanced thymic malignancies. 3. Age \> 18 years. 4. Eastern Cooperative Oncology Group (ECOG) performance status \< 2 (Karnofsky \> 60%). 5. Life expectancy of greater than 3 months. 6. Patients must have normal organ and marrow function as defined below: * leukocytes \> 3,000/mcL * absolute neutrophil count \> 1,500/mcL * platelets \> 100,000/mcL * total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) serum glutamic oxaloacetic transaminase (SGOT)/alanine aminotransferase (ALT) serum glutamic pyruvic transaminase(SGPT) less than or equal to 5 times the institutional upper limit of normal with evidence of metastatic disease to the liver or less than or equal to 3 times the institutional upper limit of normal without evidence of metastatic disease to the liver * creatinine less than or equal to 1.5 times institutional upper limits of normal OR \- creatinine clearance \> 45 mL/min/1.73 m(2) for patients with creatinine levels above institutional normal. 7. Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \> 20 mm with conventional techniques or as \> 10 mm with spiral computed tomography (CT) scan. 8. Patients must have recovered from toxicity related to prior therapy (surgery or radiation) to grade less than or equal to 1 and must be at least 28 days since any prior radiation or major surgery. Target lesions cannot be selected within previously irradiated areas, if not newly arising or clearly progressing after irradiation as proven by repeat scanning. 9. Concurrent corticosteroids for myasthenia gravis, or other paraneoplastic syndromes, or other chronic conditions are allowed. Eligibility of patients receiving any medications or substances known to affect or with the potential to affect the activity or pharmacokinetics of belinostat or cisplatin, doxorubicin or cyclophosphamide will be determined following review of their case by the Principal Investigator. Efforts should be made to switch patients with brain metastases who are taking enzyme-inducing anticonvulsant agents to other medications. 10. The effects of belinostat on the developing human fetus are unknown. For this reason and because histone deacetylase inhibitors (HDAC) inhibitors as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. 11. Ability to understand and the willingness to sign a written informed consent document. Inclusion of Women and Minorities Both men and women of all races and ethnic groups are eligible for this trial EXCLUSION CRITERIA: 1. Patients who have had major surgery or radiotherapy within 3 weeks of enrollment. 2. Patients may not be receiving any other investigational agents. 3. Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. However, patients who have had treatment for their brain metastases and whose brain metastatic disease status has remained stable for at least 1 month without steroids may be enrolled at the discretion of the principal investigator. 4. History of allergic reactions attributed to compounds of similar chemical or biologic composition to belinostat or other agents used in study. 5. Patients with prior treatment with drugs of the HDAC inhibitor class are excluded, except for valproic acid (VPA) where prior treatment is accepted as long as it is not within the last 2 weeks before enrolment. 6. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. 7. Pregnant women are excluded from this study because belinostat is an HDAC inhibitor with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with belinostat, breastfeeding should be discontinued if the mother is treated with belinostat. These potential risks may also apply to other agents used in this study. 8. Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with belinostat. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. 9. Marked baseline prolongation of Q wave, T wave (QT)/corrected QT interval (QTc) interval, e.g., repeated demonstration of a QTc interval \> 500 ms; Long QT Syndrome. Patients taking medications that may cause QTc prolongation will be eligible as long as they comply with the recommendations in appendix D. 10. History of another invasive malignancy in the last five years. Adequately treated non-invasive, non-melanoma skin cancers as well as in situ carcinoma of the cervix will be allowed. 11. Patients with tumor amenable to potentially curative therapy as assessed by the investigator.