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Restructuring and Integration Expense - Schedule of Severance and Employee Benefit Costs (Details) - USD ($)
$ in Millions
 3 Months Ended 6 Months Ended
Dec. 03, 2022
Nov. 27, 2021
Dec. 03, 2022
Nov. 27, 2021
Changes in Restructuring Liability Balance [Roll Forward]        
Integration Costs $ 14.7 $ 0.0 $ 15.2 $ 0.0
Knoll Integration        
Changes in Restructuring Liability Balance [Roll Forward]        
Integration Costs 4.1 $ 40.2 8.7 95.8
Total | Knoll Integration        
Changes in Restructuring Liability Balance [Roll Forward]        
Beginning balance     1.4  
Integration Costs     4.2  
Amounts Paid     (4.9)  
Non-cash costs     (0.2)  
Ending balance 0.5   0.5  
Severance and Employee Benefit        
Changes in Restructuring Liability Balance [Roll Forward]        
Beginning balance     0.0  
Amounts Paid     (2.6)  
Ending balance 12.6   12.6  
Severance and Employee Benefit | Knoll Integration        
Changes in Restructuring Liability Balance [Roll Forward]        
Beginning balance     1.4  
Integration Costs     1.4 $ 46.4
Amounts Paid     (2.1)  
Non-cash costs     (0.2)  
Ending balance 0.5   0.5  
Exit and Disposal Activities | Knoll Integration        
Changes in Restructuring Liability Balance [Roll Forward]        
Beginning balance     0.0  
Integration Costs     2.8  
Amounts Paid     (2.8)  
Non-cash costs     0.0  
Ending balance $ 0.0   $ 0.0