• STEP 1 REGISTRATION AND RANDOMIZATION

• Patients must be \>= 18 years of age

• Patient must have the ability to understand and the willingness to sign a written informed consent document. Patients with impaired decision-making capacity (IDMC) who have a legally authorized representative (LAR) or caregiver and/or family member available will also be considered eligible

• Patient must have a diagnosis of high grade upper tract urothelial carcinoma expected within 14 weeks (98 days) prior to registration/randomization with one of the following:

‣ Biopsy (gold standard, preferred) and either upper urinary tract mass on cross-sectional imaging or

⁃ Tumor directly visualized during upper urinary tract endoscopy

⁃ High grade cytology and clinically estimated invasive upper urinary tract mass on cross-sectional imaging (e.g., including presence of tumor-related hydronephrosis) or tumor directly visualized during upper urinary tract endoscopy

• NOTE: Universal histologic testing of UTUC with additional studies, such as immunohistochemistry or microsatellite instability, is strongly recommended to identify patients with high probability of Lynch-related or other germline mutation related cancers whom clinicians should refer for genetic counseling and germline testing (this is not required for eligibility)

‣ Due to the anatomy of upper urinary tract and lack of muscularis propria, pathologic evidence of cT2 on biopsy is usually not possible

• Leukocytes \>= 3,000/mcL (obtained =\< 14 days prior to registration/randomization)

• Platelets \>= 100,000/mcL (obtained =\< 14 days prior to registration/randomization)

• Total bilirubin =\< 1.2 mg/dL (or ≤ 2 mg/dLfor patients with Gilbert's disease)

• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2 x institutional ULN (obtained =\< 14 days prior to registration/randomization)

• Hemoglobin (Hgb) \>= 9 g/dL (obtained =\< 14 days prior to registration/randomization)

‣ NOTE: Packed red blood transfusion is allowed to achieve this parameter as per treating investigator

• Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months prior to registration/randomization are eligible for this trial

‣ NOTE: These patients must be stable on their anti-retroviral regimen with evidence of at least two undetectable viral loads within the past 6 months on the same regimen; the most recent undetectable viral load must be within the past 12 weeks. They must have a CD4 count of greater than 250 cells/mcL over the past 6 months on this same anti-retroviral regimen and must not have had a CD4 count \< 200 cells/mcL over the past 2 years, unless it was deemed related to the cancer and/or chemotherapy induced bone marrow suppression. They must not be currently receiving prophylactic therapy for an opportunistic infection and must not have had an opportunistic infection within the past 6 months

⁃ NOTE: For patients who have received chemotherapy in the past 6 months, a CD4 count \< 250 cells/mcL during chemotherapy is permitted as long as viral loads were undetectable during this same chemotherapy. They must have an undetectable viral load and a CD4 count \>= 250 cells/mcL within 7 days of registration/randomization

• For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

‣ NOTE: Testing for HIV, hepatitis B or hepatitis C is not required unless clinically indicated

• Patients with a history of hepatitis C virus (HCV) infection must have been treated and have undetectable viral load. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load

• Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better

• Patient must have a body weight of \> 30 kg

• Patient must have life expectancy of \>= 12 weeks

• Patient must have creatinine clearance \> 15 ml/min as estimated by Cockcroft-Gault formula or glomerular filtration rate (GFR) \> 15 ml/min/1.73m\^2 within 28 days prior to registration/randomization

‣ NOTE: Patients will be assigned to cisplatin-ineligible and cisplatin-eligible cohorts based on their creatinine clearance, Eastern Cooperative Oncology Group (ECOG) performance status, and grade (if any) of peripheral neuropathy and/or hearing loss in keeping with recommended cisplatin contraindications. Patients who are cisplatin-eligible will be randomized to either Arm A or Arm B and patients who are cisplatin-ineligible will be registered to Arm C

• Patients that meet any of the following four criteria will be registered to the cisplatin-ineligible Arm C if they meet other eligibility criteria:

‣ Creatinine clearance \> 15 ml/min and =\< 50 ml/min (estimated by Cockcroft-Gault formula) or GFR \> 15ml/min/1.73m\^2 and ≤ 50 ml/min/1.73 m\^2

⁃ Hearing loss \>= 3

⁃ Neuropathy \>= 2

⁃ ECOG performance status 2

∙ In addition, the patient must have an absolute neutrophil count (ANC) \>= 1,000/mcL obtained =\< 14 days prior to registration

∙ Patients that meet all of the following four criteria will be randomized to the cisplatin-eligible Arm A or Arm B:

‣ Creatinine clearance of \> 50ml/min (estimated by Cockcroft-Gault formula) or GFR \> 50ml/min/1.73m\^2

⁃ ECOG performance status 0-1

⁃ Hearing loss grade 0-2

⁃ Neuropathy 0-2

∙ In addition, the patient must have an absolute neutrophil count (ANC) \>= 1,500/mcL obtained =\< 14 days prior to randomization

∙ Also, the patient must have left ventricular ejection fraction (LVEF) \>= 50% by (either multigated acquisition scan \[MUGA\] or 2-D echocardiogram) obtained within obtained within 28 days prior to randomization