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Restructuring and Integration Expense - Additional Information (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Mar. 04, 2023	Feb. 26, 2022	Mar. 04, 2023	Feb. 26, 2022
Restructuring Cost and Reserve [Line Items]
Integration costs	$ 4.6	$ 0.0	$ 19.8	$ 0.0
Impairment of Fully	37.2
Knoll Integration
Restructuring Cost and Reserve [Line Items]
Integration costs	4.0	$ 5.9	12.7	101.7
Knoll Integration | Severance and Employee Benefit
Restructuring Cost and Reserve [Line Items]
Integration costs			3.1	49.9
Knoll Integration | Exit and Disposal Activities
Restructuring Cost and Reserve [Line Items]
Integration costs			3.6
Knoll Integration | Other Restructuring
Restructuring Cost and Reserve [Line Items]
Integration costs			6.0	22.9
Knoll Integration | Non-Cash Asset Impairments
Restructuring Cost and Reserve [Line Items]
Integration costs				15.5
Knoll Integration | Non-Cash Debt Extinguishment
Restructuring Cost and Reserve [Line Items]
Integration costs				$ 13.4
Knoll Integration | Knoll
Restructuring Cost and Reserve [Line Items]
Restructuring and related cost, expected cost	140.0		140.0
2023 Restructuring Plan | Severance and Employee Benefit
Restructuring Cost and Reserve [Line Items]
Integration costs	$ 4.6		19.8
2023 Restructuring Plan | Severance and Employee Benefit | Minimum
Restructuring Cost and Reserve [Line Items]
Cost savings			30.0
2023 Restructuring Plan | Severance and Employee Benefit | Maximum
Restructuring Cost and Reserve [Line Items]
Cost savings			$ 35.0

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