Restructuring and Integration Expense - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Jun. 03, 2023	May 28, 2022	May 29, 2021
Restructuring Cost and Reserve [Line Items]
Restructuring expenses	$ 34.4	$ 0.0	$ 2.7
Knoll Integration
Restructuring Cost and Reserve [Line Items]
Restructuring expenses	18.0	107.9
Knoll Integration \| Severance and Employee Benefit
Restructuring Cost and Reserve [Line Items]
Restructuring expenses	3.6	51.1
Knoll Integration \| Non-Cash Asset Impairments
Restructuring Cost and Reserve [Line Items]
Restructuring expenses	5.9	15.5
Knoll Integration \| Other Restructuring
Restructuring Cost and Reserve [Line Items]
Restructuring expenses	8.5	27.9
Knoll Integration \| Non Cash Debt Extinguishment
Restructuring Cost and Reserve [Line Items]
Restructuring expenses		13.4
2023 Restructuring Plan
Restructuring Cost and Reserve [Line Items]
Restructuring expenses	34.0	$ 0.0
2023 Restructuring Plan \| Severance and Employee Benefit
Restructuring Cost and Reserve [Line Items]
Restructuring expenses	27.9
2023 Restructuring Plan \| Non-Cash Asset Impairments
Restructuring Cost and Reserve [Line Items]
Restructuring expenses	6.1
2023 Restructuring Plan \| Exit and Disposal Activities
Restructuring Cost and Reserve [Line Items]
Restructuring expenses	6.1
Minimum \| 2023 Restructuring Plan
Restructuring Cost and Reserve [Line Items]
Projected annualized expense reduction	30.0
Maximum \| Knoll Integration \| Knoll
Restructuring Cost and Reserve [Line Items]
Future restructuring costs expected	140.0
Maximum \| 2023 Restructuring Plan
Restructuring Cost and Reserve [Line Items]
Projected annualized expense reduction	$ 35.0