Restructuring and Integration Expense - Schedule of Severance and Employee Benefit Costs (Details) - USD ($) $ in Millions	3 Months Ended
	Sep. 02, 2023	Sep. 03, 2022
Changes in Restructuring Liability Balance [Roll Forward]
Integration Costs	$ 5.2	$ 0.5
Knoll Integration
Changes in Restructuring Liability Balance [Roll Forward]
Integration Costs	3.9	4.6
Total | Knoll Integration
Changes in Restructuring Liability Balance [Roll Forward]
Beginning balance	2.9
Integration Costs	3.4
Amounts Paid	(3.5)
Non-cash costs	(1.3)
Ending balance	1.5
Severance and Employee Benefit | Knoll Integration
Changes in Restructuring Liability Balance [Roll Forward]
Beginning balance	2.9
Integration Costs	0.0	$ 1.2
Amounts Paid	(1.4)
Non-cash costs	0.0
Ending balance	1.5
Exit and Disposal Activities | Knoll Integration
Changes in Restructuring Liability Balance [Roll Forward]
Beginning balance	0.0
Integration Costs	3.4
Amounts Paid	(2.1)
Non-cash costs	(1.3)
Ending balance	$ 0.0