Restructuring and Integration Expense - Schedule of Severance and Employee Benefit Costs (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Dec. 02, 2023	Dec. 03, 2022	Dec. 02, 2023	Dec. 03, 2022
Changes in Restructuring Liability Balance [Roll Forward]
Integration Costs	$ 1.8	$ 14.7	$ 7.0	$ 15.2
Knoll Integration
Changes in Restructuring Liability Balance [Roll Forward]
Integration Costs	6.9	$ 4.1	10.8	8.7
Total | Knoll Integration
Changes in Restructuring Liability Balance [Roll Forward]
Beginning balance			2.9
Integration Costs			8.7
Amounts Paid			(6.3)
Non-cash costs			(2.6)
Ending balance	2.7		2.7
Severance and Employee Benefit | Knoll Integration
Changes in Restructuring Liability Balance [Roll Forward]
Beginning balance			2.9
Integration Costs			0.0	$ 1.4
Amounts Paid			(1.6)
Non-cash costs			0.0
Ending balance	1.3		1.3
Exit and Disposal Activities | Knoll Integration
Changes in Restructuring Liability Balance [Roll Forward]
Beginning balance			0.0
Integration Costs			8.7
Amounts Paid			(4.7)
Non-cash costs			(2.6)
Ending balance	$ 1.4		$ 1.4