Chemotherapy Before Surgery in Treating Patients With High Grade Upper Urinary Tract Cancer

Inclusion Criteria: * Patients must have high grade upper tract urothelial carcinoma proven by one of the following: * Biopsy; * Urinary cytology with a 3-dimensional upper urinary tract mass on cross-sectional imaging; or * Urinary cytology and a mass visualized during upper urinary tract endoscopy * Patients must have a creatinine clearance \>= 30 ml/min as determined by Cockcroft-Gault calculation or 24-hour urine creatinine clearance measurement within 28 days of registration to be eligible for the study * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Patients must have a left ventricular ejection fraction (LVEF) \>= 50% by (either multigated acquisition \[MUGA\] or 2-dimensional \[2-D\] echocardiogram) within 28 days of registration * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelets \>= 100,000/mm\^3 * Hemoglobin (HgB) \>= 9 * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 2 X institutional upper limit of normal (ULN) * Bilirubin within institutional normal limits (or \< 2.5 X the ULN for patients with Gilbert's disease) * Patients with concomitant primaries of the bladder/urethra are allowed, as long as these sites are surgically resected and non-invasive cancers (\< cT1N0) * Patients may have a history of resectable urothelial cancer (including neoadjuvant chemotherapy) as long as patients m…