Segment Analysis - Reportable Segments (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2023	Dec. 31, 2022	Sep. 30, 2023
Segment Reporting Information [Line Items]
Total revenues	$ 19,573.0	$ 13,011.6
Operating revenues	784.2	654.8
Net operating revenues (loss)	421.6	382.0
Net contribution	336.8	291.6
Segment income	216.1	172.9
Net operating revenues (loss) within Corporate	(15.6)	(11.1)
Overhead costs and expenses	(104.8)	(89.7)
Gain on acquisition	0.0	23.5
Income before tax	95.7	95.6
Assets	23,244.8		$ 21,938.7
Corporate
Segment Reporting Information [Line Items]
Total revenues	9.2	12.8
Operating revenues	9.2	12.8
Net operating revenues (loss)	(15.6)	(11.1)
Assets	839.0		812.3
Eliminations
Segment Reporting Information [Line Items]
Total revenues	(12.2)	(9.8)
Operating revenues	(12.2)	(9.8)
Commercial
Segment Reporting Information [Line Items]
Net contribution	126.4	115.7
Segment income	87.2	82.8
Commercial | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	18,978.0	12,293.5
Operating revenues	198.4	182.4
Net operating revenues (loss)	163.4	152.7
Assets	4,712.7		4,676.3
Institutional
Segment Reporting Information [Line Items]
Net contribution	100.2	94.6
Segment income	65.2	62.0
Institutional | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	435.7	343.5
Operating revenues	435.7	343.5
Net operating revenues (loss)	148.6	143.2
Assets	16,140.9		15,059.3
Retail
Segment Reporting Information [Line Items]
Net contribution	62.6	39.2
Segment income	28.7	(4.2)
Retail | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	101.7	316.2
Operating revenues	92.5	70.5
Net operating revenues (loss)	67.0	43.9
Assets	1,138.2		1,014.2
Payments
Segment Reporting Information [Line Items]
Net contribution	47.6	42.1
Segment income	35.0	32.3
Payments | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	60.6	55.4
Operating revenues	60.6	55.4
Net operating revenues (loss)	58.2	$ 53.3
Assets	$ 414.0		$ 376.6