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Restructuring and Integration Expense - Schedule of Restructuring Rollforward (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended 24 Months Ended
Feb. 26, 2022
Feb. 27, 2021
Feb. 26, 2022
Feb. 27, 2021
Feb. 26, 2022
Changes in Restructuring Liability Balance [Roll Forward]          
Restructuring Costs $ 0.0 $ 0.3 $ 0.0 $ 1.5  
Americas Contract          
Changes in Restructuring Liability Balance [Roll Forward]          
Restructuring Costs 0.0 0.2 0.0 2.6  
International Contract          
Changes in Restructuring Liability Balance [Roll Forward]          
Restructuring Costs 0.0 0.1 0.0 (1.1)  
Global Retail:          
Changes in Restructuring Liability Balance [Roll Forward]          
Restructuring Costs 0.0 0.0 0.0 0.0  
Knoll          
Changes in Restructuring Liability Balance [Roll Forward]          
Restructuring Costs 0.0 0.0 0.0 0.0  
Knoll Integration          
Changes in Restructuring Liability Balance [Roll Forward]          
Restructuring Costs 5.9 0.0 101.7 0.0  
Knoll Integration | Americas Contract          
Changes in Restructuring Liability Balance [Roll Forward]          
Restructuring Costs 0.5 0.0 4.9 0.0  
Knoll Integration | International Contract          
Changes in Restructuring Liability Balance [Roll Forward]          
Restructuring Costs 0.4 0.0 1.1 0.0  
Knoll Integration | Global Retail:          
Changes in Restructuring Liability Balance [Roll Forward]          
Restructuring Costs 0.0 0.0 0.5 0.0  
Knoll Integration | Knoll          
Changes in Restructuring Liability Balance [Roll Forward]          
Restructuring Costs 2.6 0.0 59.0 0.0  
Knoll Integration | Corporate          
Changes in Restructuring Liability Balance [Roll Forward]          
Restructuring Costs 2.4 $ 0.0 36.2 $ 0.0  
Other Restructuring Plans          
Changes in Restructuring Liability Balance [Roll Forward]          
Beginning balance     1.5    
Restructuring Costs     0.0    
Amounts Paid     (0.5)    
Ending balance 1.0   1.0   $ 1.0
Severance and Employee Benefit | Knoll Integration          
Changes in Restructuring Liability Balance [Roll Forward]          
Beginning balance     0.0    
Restructuring Costs     49.9    
Amounts Paid     (28.7)    
Non-cash costs     (14.3)    
Ending balance 6.9   6.9   6.9
Severance and Employee Benefit | Other Restructuring Plans          
Changes in Restructuring Liability Balance [Roll Forward]          
Beginning balance     0.9    
Restructuring Costs     0.0    
Amounts Paid     (0.5)    
Ending balance 0.4   0.4   0.4
Severance and Employee Benefit | May 2020 Restructuring Plan          
Changes in Restructuring Liability Balance [Roll Forward]          
Beginning balance     1.0    
Restructuring Costs     0.0   3.4
Amounts Paid     (0.7)    
Ending balance 0.3   0.3   0.3
Exit and Disposal Activities | Knoll Integration          
Changes in Restructuring Liability Balance [Roll Forward]          
Beginning balance     0.0    
Restructuring Costs     15.5    
Amounts Paid     0.0    
Non-cash costs     (15.5)    
Ending balance 0.0   0.0   0.0
Exit and Disposal Activities | Other Restructuring Plans          
Changes in Restructuring Liability Balance [Roll Forward]          
Beginning balance     0.6    
Restructuring Costs     0.0    
Amounts Paid     0.0    
Ending balance 0.6   0.6   0.6
Total | Knoll Integration          
Changes in Restructuring Liability Balance [Roll Forward]          
Beginning balance     0.0    
Restructuring Costs     65.4    
Amounts Paid     (28.7)    
Non-cash costs     (29.8)    
Ending balance $ 6.9   $ 6.9   $ 6.9