Phase II Trial Of PS-341 (Bortezomib) In Patients With Previously Treated Advanced Urothelial Tract Transitional Cell Carcinoma

Inclusion Criteria: * Histologic diagnosis of transitional cell carcinoma (TCC) of the bladder, urethra, ureter or renal pelvis; histologic documentation of metastatic/recurrent disease is not required; clinical staging, but not pathological staging, is required * All patients must have received only one prior systemic chemotherapy regimen for advanced or metastatic disease (which must have included at least one of the following chemotherapy agents: cisplatin, carboplatin, paclitaxel, docetaxel or gemcitabine), with progression documented during or after that treatment; neoadjuvant as well as adjuvant combination chemotherapy is considered a systemic chemotherapy; radiosensitizing single agent chemotherapy is not considered prior systemic therapy * Patients must have completed radiotherapy (RT) or chemotherapy \>= 4 weeks prior to registration on this trial; patients must have recovered from previous treatments or returned to their baseline in the judgment of the enrolling physician * No Prior treatment with PS-341 or other proteasome inhibitors * No prior treatment with investigational agents as single agent therapy; however, the incorporation of an investigational agent into the prior systemic chemotherapy regimen is allowed * Patients must have measurable disease; * Measurable Disease is defined as lesions 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 CT scan * Non-measurable disease: Patients with ONLY non-measurable disease are not eligible for this trial * Nonmeasurable disease is defined as all other lesions, including small lesions (longest diameter \<20 mm with conventional techniques or \< 10 mm with spiral CT scan) and truly non-measurable lesions, which include the following: * Bone lesions; * Leptomeningeal disease; * Ascites; * Pleural/pericardial effusion; * Inflammatory breast disease; * Lymphangitis cutis/pulmonis; * Abdominal masses that are not confirmed and followed by imaging techniques; * Cystic lesions * Primary bladder masses * CTC (ECOG) performance status =\< 2 * Patients must have =\< grade 1 peripheral neuropathy at baseline * No known active brain metastases; patients may not have evidence of active brain metastases; screening CT or MRI is not required, unless there is clinical suspicion of brain metastases * Pregnant and/or nursing women are not eligible for this trial as chemotherapy is thought to present substantial risk to the fetus/infant; men and women of reproductive potential may not participate unless they have agreed to use an effective contraceptive method while in this study; pregnant and/or nursing women are not eligible for this trial as chemotherapy is thought to present substantial risk to the fetus/infant; men and women of reproductive potential may not participate unless they have agreed to use an effective contraceptive method while in this study * Creatinine =\< 2.5 mg/dl or measured or calculated creatinine clearance \> 30 ml/min) * ALT and AST =\< 2.5 x ULN * Total bilirubin =\< 1.8 mg/dL * Granulocytes \>= 1500/mm\^3 * Platelets \>= 100,000/mm\^3 * Hemoglobin \>= 8 g/dl