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 meet one of the following: * pT0, Tis, or T1N0 and have no evidence of disease (NED) for more than 2 years from surgery or chemotherapy; * pT2-3aN0 and NED for more than 3 years from surgery or chemotherapy; or * \> pT3b, or N+ and NED for more than 5 years from surgery or chemotherapy * Women of childbearing potential and sexually active males must use an accepted and effective method of contraception or to abstain from sexual intercourse for the duration of their participation in the study Exclusion Criteria: * Evidence of metastatic disease or clinically enlarged lymph nodes on computed tomography (CT) or magnetic resonance imaging (MRI) of the abdomen and pelvis and CT chest obtained within 28 days of registration (a negative biopsy is required for lymph nodes \> 1 cm in size to confirm lack of involvement); patients with lymph nodes \> 1 cm in whom a biopsy is deemed not feasible are not eligible; patients with elevated alkaline phosphatase or suspicious bone pain should also undergo baseline bone scans to evaluate for bone metastasis * Any component of small cell carcinoma; other variant histologies are permitted provided the predominant (\>= 50%) subtype is urothelial carcinoma * Peripheral neuropathy \> grade 2 * History of allergy or hypersensitivity to methotrexate, vinblastine, doxorubicin (doxorubicin hydrochloride), cisplatin, gemcitabine (gemcitabine hydrochloride), carboplatin or filgrastim or pegfilgrastim * Another active second malignancy other than non-melanoma skin cancers and biochemical relapsed prostate cancer; patients that have completed all necessary therapy and are considered to be at less than 30% risk of relapse are not considered to have an active second malignancy and are eligible for enrollment * Prior systemic doxorubicin for patients who have creatinine clearance that meets \>= 50 ml/min * Uncontrolled illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, myocardial infarction in last 3 months, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Known to have human immunodeficiency virus (HIV) or are on combination antiretroviral therapy * Prior radiation therapy to \>= 25% of the bone marrow for other diseases or prior systemic anthracycline therapy; prior intravesical anthracycline therapy for non-muscle invasive urothelial carcinoma of the bladder is permitted * Pregnant or breast-feeding; all females of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy; a female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months)