A Phase I/II Study of TRC105 in Metastatic Castrate Resistant Prostate Cancer (CRPC)

* INCLUSION CRITERIA: 1. Patients must have histopathological confirmation of prostate cancer by the Laboratory of Pathology of the National Cancer Institute (NCI), Pathology Department of the National Naval Medical Center or Pathology Department of Walter Reed Army Medical Center prior to entering this study. Patients whose pathology specimens are no longer available may be enrolled in the trial if the patient has a clinical course consistent with prostate cancer and available documentation from an outside pathology laboratory of the diagnosis. In cases where original tissue blocks or archival biopsy material is available, efforts will be made to contact referring physicians and outside pathology departments to have the material forwarded to the research team for use in correlative studies. 2. Patients must have metastatic progressive castrate-resistant prostate cancer defined as progressive disease (see below) despite surgical castration or ongoing use of gonadotropin-releasing hormone agonists with confirmed castrate levels of testosterone. Criteria of progression for trial eligibility are defined from the Prostate Cancer Clinical Trials Working Group-2. Clinically progressive prostate cancer must be evidenced and documented by any of the following parameters: 1. Two consecutively rising prostate specific antigen (PSA) values at a minimum of 1-week intervals (2.0 ng/mL is the minimum starting value for PSA) 2. Appearance of one or more new lesion on bone scans 3. Progressive measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 Patients on flutamide for at least 6 months must have disease progression at least 4 weeks after withdrawal. Patients on bicalutamide or nilutamide for at least 6 months must have progression at least 6 weeks after withdrawal. All patients enrolled will be required to have measurable or non-measurable disease on imaging studies. 4\. Age greater than or equal to 18 years. 5\. Life expectancy of greater than 3 months. 6\. Eastern Cooperative Oncology Group (ECOG) performance status 0-2. 7\. Patients must have normal organ and marrow function as defined below: * Absolute neutrophil count greater than or equal to 1,500/mcL * Platelets greater than or equal to 100,000/mcL * Total bilirubin less than or equal to 1.5 times upper normal limits or less than 3 mg/dl in subjects with Gilbert's Syndrome * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) less than or equal to 2.5 times upper limit of normal * Creatinine less than or equal to 1.5 times upper normal limits OR creatinine clearance greater than or equal to 40 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal, as calculated by the Cockcroft Gault formula. 8\. Patients must have recovered from any acute toxicity related to prior therapy, including surgery. Toxicity should be less than or equal to grade 1 or returned to baseline. 9\. All patients who have not undergone bilateral surgical castration must continue suppression of testosterone production by appropriate usage of gonadotropin releasing hormone (GnRH) agonists or antagonists. 10\. Patients must not have other invasive malignancies (within the past 2 years with the exception of non-melanoma skin cancers or non-invasive bladder cancer). 11\. Enrolled patients must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, the duration of study participation and 3 months after the end of the treatment. 12\. Patient must be able to understand and willing to sign a written informed consent document. 13\. Patients on a stable dose of steroids of 10 mg/day or less can continue on steroids if they are on peptic ulcer disease prophylaxis with an H2-blocker or proton pump inhibitor. EXCLUSION CRITERIA: 1. Patients who have had chemotherapy, large field radiotherapy, or major surgery must wait 3 weeks prior to entering the study. 2. Patients may not be receiving any agents not approved by the Food and Drug Administration (FDA) within the past 4 weeks. 3. Patients with known brain metastases will 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. 4. Proteinuria, as demonstrated by a 24 hour protein of (Bullet) 2000 mg. Urine protein will be screened by urine protein-creatinine ratio (UPC). For UPC ratio \> 1.0, a 24-hour urine protein will need to be obtained and the level should be \< 2000 mg for patient enrollment. 5. Uncontrolled intercurrent illness including, but not limited to, hypertension (systolic blood pressure (BP) \> 160, diastolic BP \> 100), ongoing or active systemic infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia or psychiatric illness/social situations that would limit compliance with study requirements. 6. Thrombolytic or treatment-dose anticoagulant use within 10 days prior to first dose with TRC105. 7. Hemorrhage within 30 days of dosing. 8. History of peptic ulcer disease or gastritis within 6 months of TRC105 administration, unless patient has received adequate treatment for peptic ulcer disease and has evidence of complete resolution documented by esophagogastroduodenoscopy (EGD). 9. Corrected QT interval (QTc) \> 500 msec. 10. Known human immunodeficiency virus (HIV)-positive patients are excluded. 11. History of hypersensitivity reaction to human or mouse antibody products. 12. Patients with a history of familial bleeding disorders. 13. Patients with a history of hereditary hemorrhagic telangiectasia (Osler-Weber-Rendu syndrome). 14. Use of non-steroidal anti-inflammatory drugs (NSAIDs) beginning 14 days prior to the first TRC105 dose, with the exception of aspirin when clinically indicated.