TRC105 in Adults With Advanced/Metastatic Urothelial Carcinoma

* INCLUSION CRITERIA: * Patients must have a diagnosis of urothelial carcinoma of the bladder, urethra, ureter, or renal pelvis, with histological confirmation at the Laboratory of Pathology of the NCI (National Cancer Institute), NIH (National Institutes of Health). * Patients must have progressive metastatic disease. Progressive disease will be defined as new or progressive lesions on cross-sectional imaging. Patients must have at least: * One measurable site of disease (according to RECIST criteria) that has not been previously irradiated. If the patient has had previous radiation to the marker lesion(s), there must be evidence of progression since the radiation. * Or, appearance of one new bone lesion. * Patients must have been previously treated, as defined by the following: * Treatment with at least one prior cytotoxic agent (which must have included at least one of the following: cisplatin, carboplatin, paclitaxel, docetaxel, or gemcitabine), administered in the perioperative or metastatic setting and may have been administered sequentially (e.g., first-line treatment followed by second-line treatment at time of progression) or as part of a single regimen. * 18 years of age or older * ECOG (Eastern Cooperative Oncology Group) performance status of \< 2 or Karnofsky Performance Status greater than or equal to 60% * Resolution of all acute toxic effects of prior chemotherapy, radiotherapy, or surgical procedure to NCI CTCAE (Common Terminology Criteria in Adverse Events) grade less than or equal to 1 or baseline * Adequate organ function as defined by the following criteria: * Serum aspartate transaminase (AST (Aspartate transaminase); serum glutamic oxaloacetic transaminase \[SGOT (serum glutamic oxaloacetic)\]) and serum alanine transaminase (ALT (alanine transaminase); serum glutamic pyruvic transaminase \[SGPT (serum glutamic pyruvic transaminase)\]) less than or equal to 2.5 times the upper limit of normal (ULN); 5.0 times the ULN in cases of liver metastases * Total serum bilirubin less than or equal to 1.5 mg/dL (unless elevation from Gilbert's disease or similar syndrome due to slow conjugation of bilirubin) * Absolute neutrophil count (ANC) greater than or equal to 1000/microL * Platelets greater than or equal to 100,000/microL * Serum creatinine less than or equal to 2.0 mg/dl or calculated creatinine clearance (CrCl) greater than or equal to 30 mL/min * Hemoglobin \> 9gm/dL * PT (prothrombin time), aPTT (activated partial thromboplastin time) must be within normal range * Patients on anticoagulants may be enrolled as long as the INR (International normalized ratio) does not exceed 3. EXCLUSION CRITERIA: * Receipt of an investigational agent within 4 weeks prior to first dose with TRC105 * Major surgery including open biopsy or systemic therapy \< 4 weeks prior to first dose with TRC105 * Radiation therapy (except small field) \< 3 weeks prior to first dose with TRC105 * Small field radiation therapy \< 2 weeks prior to first dose with TRC105 * Minor surgical procedures within 2 weeks * Uncontrolled chronic hypertension (systolic \> 140 or diastolic \> 90mm Hg despite optimal therapy) * Brain metastasis, or leptomeningeal disease because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * Unstable angina, MI, symptomatic congestive heart failure, cerebrovascular accident, transient ischemic attack, arterial embolism, pulmonary embolism, DVT (deep vein thrombosis), PTCA (percutaneous transluminal coronary angioplasty) or CABG (coronary artery bypass graft) within the past 6 months * Cardiac arrhythmias of NCI CTCAE grade greater than or equal to 2 within the last month * Serious, non-healing wound, ulcer, or bone fracture * Known active hepatitis * Hemorrhage within 30 days of dosing or history of persistent gross hematuria * Known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS) related illness * History of hypersensitivity reaction to human or mouse antibody products * Pregnancy or breastfeeding. Female patients must be surgically sterile (i.e.: hysterectomy) or be postmenopausal, or must agree to use effective contraception during the study and for 3 months following last dose of TRC105. All female patients of reproductive potential must have a negative pregnancy test (serum) within 7 days prior to first dose. Male patients must be surgically sterile or must agree to use effective contraception during the study and for 3 months following last dose of TRC105. The definition of effective contraception will be based on the judgment of the Principal Investigator or a designated associate. * Other severe acute or chronic medical or psychiatric condition, or laboratory abnormality that may increase the risk associated with study participation or study drug administration, or may interfere with the interpretation of study results, and in the judgment of the Investigator would make the patient inappropriate for entry into this study * History of peptic ulcer disease, unless a subsequent endoscopy has confirmed complete resolution of the ulcer * History of acquired or inherited hypocoagulopathies (bleeding risk), including but not limited to hereditary hemorrhagic telangiectasis.