FORAGER-1: A Study of Vepugratinib (LY3866288; LOXO-435) in Participants With Cancer With a Change in a Gene Called FGFR3

Inclusion Criteria: * Cohort A1, C1, D1, and D2: Locally advanced or metastatic solid tumor malignancy with a qualifying FGFR3 alteration. * Cohort A2, B2, B5 and B7: Urothelial cancer (UC) that is locally advanced or metastatic with a qualifying FGFR3 genetic alteration. * Cohorts B1 and B4: Urothelial cancer that is locally advanced or metastatic and have received prior erdafitinib. * Cohort B6: Muscle Invasive Bladder Cancer with a qualifying FGFR3 alteration. * Cohort B7: Urothelial cancer that is locally advanced or metastatic with a qualifying FGFR3 genetic alteration and expression of human epidermal growth factor receptor 2 (HER2). * Cohort B8: Low Grade Intermediate Risk Non-Muscle Invasive Bladder cancer and a qualifying FGFR3 genetic alteration. * Measurability of disease: * Cohort A1, D1, and D2: Measurable or non-measurable disease as defined by Response Evaluation Criteria in Solid Tumors v 1.1 (RECIST v1.1). * Cohorts A2, B1, B2, B4, B5, B7, and C1: Measurable disease required as defined by RECIST v1.1. * Cohort B8: Baseline disease which includes at least 1 lesion. * Have an Eastern Cooperative Oncology Group (ECOG) performance status of: * 0 or 1 for Cohorts A1, A2, B5, B6, B7, and B8. * Less than or equal to 2 for Cohorts B1, B2, B4, C1, DI and D2. * Cohort B6: Must be eligible for radical cystectomy plus pelvic lymph node dissection and agree to undergo curative intent standard radical cystectomy plus pelvic lymph node dissection. Exclusion Criteria: * Participants with primary central nervous system (CNS) malignancy. * Untreated or uncontrolled CNS metastases. * Current evidence of corneal keratopathy or retinal disorder. Individuals with asymptomatic ophthalmic conditions may be eligible. * Any serious unresolved toxicities from prior therapy. * Significant cardiovascular disease. * Prolongation of the QT interval corrected for heart rate using Fridericia's formula (QTcF). * Active uncontrolled systemic infection or other clinically significant medical conditions. * Participants who are pregnant, lactating, or plan to breastfeed during the study or within 6 months of the last dose of study treatment. Participants who have stopped breastfeeding may be enrolled. * Cohort D1 only: * Have had renal transplantation. * Have a known history of nephrotic syndrome. * Have uncontrolled fluid overload, including clinically significant ascites, pleural effusion, or peripheral edema. * Have uncontrolled hypertension. * Are on hemodialysis or similar. * Cohort D2 only: * Have a history of: * Ventricular tachycardia or ventricular fibrillation. * Hypertrophic obstructive cardiomyopathy unless managed concurrently with atrial fibrillation. * Wolff-Parkinson-White syndrome. * Second- or third-degree atrioventricular block unless a functioning pacemaker is in place. * Heart rate less than (\<) 50 bpm. * Have any of these medical conditions: * Severe respiratory insufficiency. * Sleep apnea syndrome. * Myasthenia gravis. * Acute narrow-angle glaucoma. * Active liver disease or clinically significant hepatic impairment. * History of myopathy or rhabdomyolysis with any HMG-CoA reductase inhibitor.