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Segment Analysis - Schedule of Segment Reporting Information (Details) - USD ($)
$ in Millions
3 Months Ended
Dec. 31, 2024
Dec. 31, 2023
Sep. 30, 2024
Segment Reporting Information [Line Items]      
Total revenues $ 27,935.3 $ 19,573.0  
Operating revenues 944.3 784.2  
Net operating revenues (loss) 492.1 421.6  
Net contribution 401.4 336.8  
Segment income 271.3 216.1  
Net operating loss within Corporate (21.1) (15.6)  
Overhead costs and expenses (133.3) (104.8)  
Income before tax 116.9 95.7  
Assets 29,585.3   $ 27,466.3
Corporate      
Segment Reporting Information [Line Items]      
Total revenues 11.1 9.2  
Operating revenues 11.1 9.2  
Net operating revenues (loss) (21.1) (15.6)  
Assets 974.1   1,123.5
Eliminations      
Segment Reporting Information [Line Items]      
Total revenues (20.9) (12.2)  
Operating revenues (20.9) (12.2)  
Commercial      
Segment Reporting Information [Line Items]      
Net contribution 145.7 126.4  
Segment income 102.2 87.2  
Commercial | Operating Segments      
Segment Reporting Information [Line Items]      
Total revenues 27,209.0 18,978.0  
Operating revenues 232.3 198.4  
Net operating revenues (loss) 189.2 163.4  
Assets 5,690.7   5,387.0
Institutional      
Segment Reporting Information [Line Items]      
Net contribution 117.8 100.2  
Segment income 78.1 65.2  
Institutional | Operating Segments      
Segment Reporting Information [Line Items]      
Total revenues 539.6 435.7  
Operating revenues 539.6 435.7  
Net operating revenues (loss) 174.0 148.6  
Assets 21,571.4   19,492.9
Self-Directed/Retail      
Segment Reporting Information [Line Items]      
Net contribution 91.6 62.6  
Segment income 56.9 28.7  
Self-Directed/Retail | Operating Segments      
Segment Reporting Information [Line Items]      
Total revenues 138.4 101.7  
Operating revenues 124.1 92.5  
Net operating revenues (loss) 94.6 67.0  
Assets 930.8   1,024.1
Payments      
Segment Reporting Information [Line Items]      
Net contribution 46.3 47.6  
Segment income 34.1 35.0  
Payments | Operating Segments      
Segment Reporting Information [Line Items]      
Total revenues 58.1 60.6  
Operating revenues 58.1 60.6  
Net operating revenues (loss) 55.4 $ 58.2  
Assets $ 418.3   $ 438.8