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Restructuring and Integration Expense - Narrative (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
Assets held for sale 3.5 0.0  
Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 23.5 18.0  
Knoll Integration | Exit and Disposal Activities      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 19.4 5.9  
Knoll Integration | Other Restructuring      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 4.1 8.5  
Knoll Integration | Severance and Employee Benefit      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 0.0 3.6  
2024 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 30.8    
Future restructuring costs expected 0.0    
2024 Restructuring Plan | Exit and Disposal Activities      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 11.5    
2024 Restructuring Plan | Severance and Employee Benefit      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 19.3    
2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 0.0 34.0  
Future restructuring costs expected 0.0    
2023 Restructuring Plan | Exit and Disposal Activities      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 0.0    
2023 Restructuring Plan | Severance and Employee Benefit      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses 0.0 27.9  
2023 Restructuring Plan | Non-Cash Asset Impairments      
Restructuring Cost and Reserve [Line Items]      
Restructuring expenses   $ 6.1  
Knoll | Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Future restructuring costs expected $ 150.0