Mitoxantrone, Prednisone Plus Sorafenib in Taxane-Refractory Metastatic Hormone Refractory Prostate Cancer (HRPC)

Inclusion Criteria: * Voluntary written informed consent * Histopathologic diagnosis of prostatic adenocarcinoma with evidence of progression despite adequate castration (testosterone \< 50 ng/dL) * Progressive disease after taxane-based chemotherapy (docetaxel or paclitaxel, single agent or combination regimens, weekly or every 21 day schedules) * Patients who discontinued taxane- based chemotherapy because of toxicity will be eligible as long as there is evidence of progressive disease * Minimum of 4 weeks period from last chemotherapy infusion to registration (this does not apply to steroid use which is permitted). Estramustine needs to be discontinued at least 6 weeks prior to first day of treatment on protocol * A minimum of 4 weeks off bicalutamide, nilutamide, megestrol acetate ketoconazole, diethylstilbestrol (DES). Minimum of 2 weeks off flutamide * Reductase inhibitors will be allowed if initiated at least 2 months prior to registration * No concurrent investigational therapy * Complementary and Alternative Medicine (CAM) products will be permitted as long as patients have been receiving them for at least 2 months. Initiation of new CAM products while on protocol will be discouraged. * Ongoing androgen deprivation therapy (orchiectomy, gonadotropin-releasing hormone (GnRH) agonist or antagonist) * Adequate bone marrow, liver and renal function as assessed by the following: * Hemoglobin ≥ 9.0 g/dl * Absolute neutrophil count (ANC) ≥ 1,500/mm3 * Platelet count ≥ 100,000/mm3 * Total bilirubin ≤ 1.5 times upper limit of normal (ULN) * ALT and AST ≤ 2.5 times the ULN ( ≤ 5 x ULN for patients with liver involvement) * Creatinine ≤ 1.5 times the ULN * International normalized ratio (INR) \< 1.5 or a Prothrombin (PT)/Partial thromboplastin time (PTT) within normal limits. Patients receiving anti-coagulation treatment with an agent such as warfarin or heparin may be allowed to participate. For patients on warfarin, the INR should be measured prior to initiation of sorafenib and monitored at least weekly, or as defined by the local standard of care, until INR is stable. * ECOG performance status ≤ 2 * Baseline left ventricular ejection fraction (LVEF) ≥ 50% * Life expectancy ≥ 3 months * Patients must agree to use adequate contraception prior to study entry, during the study and for at least three months after the last administration of sorafenib Exclusion Criteria: * More than one line of prior cytotoxic chemotherapy in the metastatic setting, previous adjuvant chemotherapy will be allowed * No active malignancy other than prostate cancer (except non-melanoma skin cancer) within 5 years of enrollment * Known brain metastases * Cardiac disease: Congestive heart failure \> class II New York Heart Association (NYHA). Patients must not have unstable angina or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months * Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy * Uncontrolled hypertension * Active clinically serious infection \> Common Terminology Criteria for Adverse Events (CTCAE) Grade 2 * Thrombolic or embolic events such as a cerebrovascular accident including transient ischemic attacks within the past 6 months * Pulmonary hemorrhage/bleeding event ≥ CTCAE Grade 2 within 4 weeks of first dose of study drug * Any other hemorrhage/bleeding event ≥ CTCAE Grade 3 within 4 weeks of first dose of study drug * Poorly controlled hyperglycemia * Treatment with radiotherapy within 4 weeks or treatment with radiopharmaceuticals within past 8 weeks * Patient has received other investigational drugs within 14 days before enrollment * Serious medical or psychiatric illness likely to interfere with participation in this clinical study * Serious non-healing wound or ulcer * Evidence or history of bleeding diathesis or coagulopathy * Use of St. John's Wort or rifampin * Known or suspected allergy to sorafenib or any agent given in the course of this trial * Any condition that impairs patient's ability to swallow whole pills * Any malabsorption problem