Testing the Addition of MEDI4736 (Durvalumab) to Chemotherapy Before Surgery for Patients With High-Grade Upper Urinary Tract Cancer

PRIMARY OBJECTIVES: I. To compare event-free survival (EFS) between patients with upper tract urothelial cancer (UTUC) randomized to neoadjuvant accelerated methotrexate, vinblastine, Adriamycin, cisplatin (aMVAC) alone or in combination with durvalumab. (Cisplatin eligible patients \[Arms A and B\]) II. Evaluation of pathologic complete response at radical nephroureterectomy (RNU) (pathologic complete response \[pCR\], ypT0N0/Nx). (Cisplatin ineligible patients \[Arm C\]). SECONDARY OBJECTIVES: I. To assess pathologic complete response (pCR) at surgery. (Cisplatin eligible cohort) II. Event-free survival (EFS) will be evaluated for the cisplatin ineligible cohort as a secondary endpoint. (Cisplatin ineligible cohort) III. Overall survival in all, and by post chemotherapy response (ypT0N0, yp =\< T1N0, yp \>= T2Nany). (All patients) IV. To evaluate disease-free survival (DFS) in each arm of the trial separately. (All patients) V. To evaluate cancer-specific survival of patients in each arm of the trial separately. (All patients) VI. To evaluate renal function outcomes following systemic treatment and following surgery (\[RNU) in each arm of the trial separately. (All patients) VII. To evaluate safety and tolerability of neoadjuvant aMVAC alone or in combination with durvalumab prior to RNU. (All patients) OUTLINE: Patients eligible for cisplatin are randomized to Arms A or B. Patients ineligible for cisplatin are assigned to Arm C. ARM A: Patients receive durvalumab intravenously (IV) over 60 minutes on day 1 of chemotherapy cycles 1 and 3. Patients also receive methotrexate IV over 2-3 minutes, vinblastine sulfate IV, doxorubicin IV, cisplatin IV over at least 2 hours on day 1. Treatments repeat every 14 days for up to 4 cycles in the absence of disease progression or unacceptable toxicity. Within 21- 60 days after completion of systemic treatment, patients with continued lack of radiographic presence of metastatic or unresectable disease undergo surgery. ARM B: Patients also receive methotrexate IV over 2-3 minutes, vinblastine sulfate IV, doxorubicin IV, cisplatin IV over at least 2 hours on day 1. Treatments repeat every 14 days for up to 4 cycles in the absence of disease progression or unacceptable toxicity. Within 21- 60 days after completion of systemic treatment, patients with continued lack of radiographic presence of metastatic or unresectable disease undergo surgery. ARM C: Patients receive durvalumab IV over 60 minutes on day 1 and gemcitabine hydrochloride IV over 30 minutes on days 1 and 8. Treatment repeats every 21 days for up to 4 cycles in the absence of disease progression or unacceptable toxicity. Within 21- 60 days after completion of systemic treatment patients with continued lack of radiographic presence of metastatic or unresectable disease undergo surgery. Patients also undergo tissue biopsy and blood sample collection on study, and computed tomography (CT) or magnetic resonance imaging (MRI) throughout the trial. After completion of study treatment, patients are followed up within 30 days and then every 3-6 months for up to 5 years from study entry.