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Restructuring and Integration Expense - Schedule of Severance and Employee Benefit Costs (Details) - USD ($)
$ in Millions
 12 Months Ended
Jun. 01, 2024
Jun. 03, 2023
May 28, 2022
Restructuring Cost and Reserve [Line Items]      
Integration Costs $ 30.8 $ 34.4 $ 0.0
Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Integration Costs 23.5 18.0  
Knoll Integration | Severance and Employee Benefit      
Restructuring Cost and Reserve [Line Items]      
Beginning balance 2.9    
Integration Costs 0.0 3.6  
Amounts Paid (2.9)    
Non-cash Costs 0.0    
Ending balance 0.0 2.9  
Knoll Integration | Exit and Disposal Activities      
Restructuring Cost and Reserve [Line Items]      
Beginning balance 0.0    
Integration Costs 19.4 5.9  
Amounts Paid (13.4)    
Non-cash Costs (5.3)    
Ending balance 0.7 0.0  
Knoll Integration | Severance And Employee Benefits And Exit And Disposal Activities      
Restructuring Cost and Reserve [Line Items]      
Beginning balance 2.9    
Integration Costs 19.4    
Amounts Paid (16.3)    
Non-cash Costs (5.3)    
Ending balance $ 0.7 $ 2.9