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Restructuring and Integration Expense - Schedule of Restructuring Expenses by Segment (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  
2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 34.0 0.0  
Americas Contract | Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 9.7 21.9  
Americas Contract | 2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 22.8 0.0  
International Contract and Specialty | Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 2.5 0.0  
International Contract and Specialty | 2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 1.3 0.0  
Global Retail | Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 0.2 0.0  
Global Retail | 2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 9.9 0.0  
Corporate | Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 5.6 86.0  
Corporate | 2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses $ 0.0 $ 0.0