Testing the Addition of an Anti-Cancer Immunotherapy Drug, Avelumab, to Gemcitabine and Carboplatin Chemotherapy Prior to Surgery in Muscle Invasive Urinary Tract Cancer vs. Surgery Alone in Patients Who Are Not Able to Receive Cisplatin Therapy (SWOG GAP TRIAL)

Participants must have one of the following:

* Histologically documented muscle-invasive bladder carcinoma (MIBC) from transurethral resection of bladder tumor (TURBT) within 56 days prior to registration

* Histologically confirmed high grade upper tract urothelial carcinoma (UTUC) within 56 days prior to registration, with invasion confirmed by either a mass on cross-sectional imaging or a tumor directly visualized during upper urinary tract endoscopy within 56 days prior to registration

Participants must have clinical stage T2-T4aN0M0 bladder or upper tract cancer confirmed by radiologic staging (computed tomography \[CT\] scan/magnetic resonance imaging \[MRI\] abdomen and pelvis, and CT scan/x-ray of the chest) within 56 days prior to registration

Participants must have a bone scan within 56 days prior to registration if they have bone pain or elevated serum alkaline phosphatase

Participants must have a bimanual examination under anesthesia within 56 days prior to registration

Participants must not have received prior systemic chemotherapy, immunotherapy or radiotherapy for the treatment of muscle invasive bladder cancer (MIBC) or upper tract urothelial carcinoma (UTUC). Other prior pelvic radiotherapy is allowed if it does not preclude surgery (radical cystectomy, nephroureterectomy or ureterectomy, based on location of primary tumor). Prior intravesical therapy is allowed

Participants must not have received immunosuppressive medication within 14 days prior to registration, with the exception of intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra-articular injection) systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or its equivalent

Participants must be \>= 18 years of age

Participants must have Zubrod performance status 0-2

Participants must have history and physical examination within 28 days prior to registration

Participants must be surgical candidates as deemed by the local site oncologic surgeon within 28 days prior to registration. This must be clearly documented

Participants must have a serum creatinine =\< the institutional upper limit of normal (IULN) OR measured OR calculated creatinine clearance \>= 30 mL/min using the Crockroft-Gault Formula. This specimen must have been drawn and processed within 28 days prior to registration

Participants must be deemed cisplatin-ineligible based on greater than or equal to 1 of the following:

* Zubrod performance status = 2

* Creatinine clearance (calculated by Crockroft-Gault formula or measured) 30 to \< 60 ml/min,

* Neuropathy \> grade 1

* Hearing loss \> grade 1

* Congestive heart failure \> grade 2

Hemoglobin \>= 9.0 g/dL (within 28 days prior to registration)

Absolute neutrophil count \>= 1,500/mcL (within 28 days prior to registration)

Platelets \>= 100,000/mcL (within 28 days prior to registration)

Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (within 28 days prior to registration)

Aspartate aminotransferase (AST) =\< 2.5 x institutional ULN (within 28 days prior to registration)

Alanine aminotransferase (ALT) =\< 2.5 x institutional ULN (within 28 days prior to registration)

Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, must have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification and be class 2B or better

Participants with known human immunodeficiency virus (HIV) must be on effective anti-retroviral therapy and have undetectable viral load at their most recent viral load test and within 6 months prior to registration

What this study is about