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

Inclusion Criteria: * 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 and/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 * Patients must not have any component of small cell/neuroendocrine carcinoma. Other histologic subtypes (variants) are permitted provided the half or predominant (\>= 50%) subtype is conventional urothelial carcinoma * 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/dL for 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 * Patients must not be pregnant or breast-feeding due to the potential harm to an unborn fetus and possible risk for adverse events in nursing infants with the treatment regimens being used. All patients of childbearing potential must have a blood test or urine study within 14 days prior to registration to rule out pregnancy. A patient of childbearing potential is defined as any patient, regardless of whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * Patients of childbearing potential and sexually active patients must not expect to conceive or father children, either by using accepted and effective method(s) of contraception or by abstaining from sexual intercourse from the time of registration, while on study treatment and for at least 6 months after the last dose of protocol treatment * Patients must have no evidence of metastatic disease or clinically enlarged regional lymph nodes (\>= 1.5 cm short axis) on imaging required within 28 days prior to registration (Non-regional findings \>=1.5 cm short axis that in the opinion of the investigator are not concerning for involvement based on radiographic characteristics, chronicity, avidity on positron emission tomography (PET) scan or other imaging or other criteria can be eligible based on investigator discretion). * NOTE: Patients with elevated alkaline phosphatase, calcium or suspicious bone pain/tenderness can also undergo baseline bone scan to evaluate for bone metastasis at the discretion of local provider. * Patient must meet below criteria for prior/current malignancy history: * Non-urothelial cancer malignancy history: * Patient must not have another active (or within two years) second malignancy other than resected non-melanoma skin cancers, resected in situ breast, cervical or other in situ carcinoma, and either clinically insignificant per the investigator (e.g. =\< Gleason 3+4) on active surveillance (or watchful waiting) or previously treated prostate cancer with no rising prostate specific antigen (PSA) and no plan to treat * NOTE: Patients with prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. * Urothelial cancer malignancy history: * Patient may have a history of resectable urothelial cancer as long as patients meet one of the following: * T0, Ta or Tis at any time * T1-4a N0 and no evidence of disease (NED) for more than 2 years from the latest therapy \[e.g., radical surgery, transurethral resection of bladder tumor (TURBT), radiation, chemotherapy (neoadjuvant or adjuvant, or with radiation)\]. Prior systemic immune checkpoint inhibitor is not allowed. * Patient with history of \>= pT4b, N+, and/or M1 UC is not eligible. * NOTE: Patients in whom concomitant or prior bladder/urethra predominant (\>= 50%) urothelial carcinoma have been surgically resected and demonstrated to be only Ta or carcinoma in situ (CIS) (\< cT1 N0) are eligible regardless of time elapsed * Patient must not have any uncontrolled illness including, but not limited to, ongoing or active infection including tubercu