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Restructuring and Integration Expense - Schedule of Restructuring Expenses by Segment (Details) - USD ($)
$ in Millions
 12 Months Ended
Jun. 01, 2024
Jun. 03, 2023
May 28, 2022
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses $ 30.8 $ 34.4 $ 0.0
Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 23.5 18.0  
2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 0.0 34.0  
2024 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 30.8    
Americas Contract | Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 18.6 9.7  
Americas Contract | 2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses   22.8  
Americas Contract | 2024 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 24.6    
International Contract & Specialty | Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 4.8 2.5  
International Contract & Specialty | 2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses   1.3  
International Contract & Specialty | 2024 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 4.1    
Global Retail | Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 0.0 0.2  
Global Retail | 2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses   9.9  
Global Retail | 2024 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 2.1    
Corporate | Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 0.1 5.6  
Corporate | 2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses   $ 0.0  
Corporate | 2024 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses $ 0.0