Testing Combination Erdafitinib and Enfortumab Vedotin in Metastatic Bladder Cancer After Treatment With Chemotherapy and Immunotherapy

Inclusion Criteria: * Patients must have histologically or cytologically documented locally advanced (T4b, any N; or any T, N 2-3) or metastatic (M1, Stage IV; or metastatic recurrence after locoregional treatment) urothelial carcinoma (including renal pelvis, ureters, urinary bladder, urethra). Patients with mixed histologies are required to have a dominant transitional cell pattern * Patients who had disease progression during or following treatment with at least one platinum-containing regimen (e.g., gemcitabine and cisplatin \[GC\], methotrexate, vinblastine, doxorubicin and cisplatin \[MVAC\], carboplatin and gemcitabine \[Carbo-Gem\]) and an immune checkpoint inhibitor (PD-1/ PD-L1 inhibitor including but not limited to: atezolizumab, pembrolizumab, durvalumab, avelumab, and nivolumab) * Received a first-line platinum-containing regimen in the metastatic setting or for inoperable locally advanced disease * Or received neo/adjuvant platinum-containing therapy for localized muscle-invasive UC, with recurrence/progression =\< 12 months following completion of therapy * Patients who received immune checkpoint inhibitor therapy in the neoadjuvant/adjuvant setting and had recurrent or progressive disease either during therapy or within 12 months of therapy completion are eligible. This criterion does not apply if the checkpoint inhibitor is contraindicated * Patients with metastatic urothelial carcinoma who are cisplatin-ineligible and progressed on upfront immune che…