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Restructuring and Integration Expense - Schedule of Restructuring Expenses by Segment (Details) - USD ($)
$ in Millions
 12 Months Ended
May 31, 2025
Jun. 01, 2024
Jun. 03, 2023
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses $ 14.8 $ 30.8 $ 34.4
Corporate      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 0.0 0.0  
Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 28.3 23.5 $ 18.0
Knoll Integration | Corporate      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 0.0 0.1  
2025 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 14.8    
2024 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 0.0 30.8  
North America Contract | Operating Segments      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 9.8 25.3  
North America Contract | Knoll Integration | Operating Segments      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 24.8 22.6  
International Contract | Operating Segments      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 3.3 3.4  
International Contract | Knoll Integration | Operating Segments      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 3.2 0.3  
Global Retail | Operating Segments      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 1.7 2.1  
Global Retail | Knoll Integration | Operating Segments      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses $ 0.3 $ 0.5