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Restructuring and Integration Expense - Schedule of Restructuring Rollforward (Details) - USD ($)
$ in Millions
 3 Months Ended 12 Months Ended
Aug. 28, 2021
Aug. 29, 2020
May 29, 2021
Restructuring Cost and Reserve [Line Items]      
Restructuring Costs $ 0.0 $ (1.2)  
Americas Contract      
Restructuring Cost and Reserve [Line Items]      
Restructuring Costs 0.0 1.6  
International Contract      
Restructuring Cost and Reserve [Line Items]      
Restructuring Costs 0.0 (2.8)  
Retail:      
Restructuring Cost and Reserve [Line Items]      
Restructuring Costs 0.0 0.0  
Knoll      
Restructuring Cost and Reserve [Line Items]      
Restructuring Costs 0.0 0.0  
Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring Costs 55.6 0.0  
Knoll Integration | Americas Contract      
Restructuring Cost and Reserve [Line Items]      
Restructuring Costs 1.0 0.0  
Knoll Integration | International Contract      
Restructuring Cost and Reserve [Line Items]      
Restructuring Costs 0.0 0.0  
Knoll Integration | Retail:      
Restructuring Cost and Reserve [Line Items]      
Restructuring Costs 0.0 0.0  
Knoll Integration | Knoll      
Restructuring Cost and Reserve [Line Items]      
Restructuring Costs 29.4 0.0  
Knoll Integration | Corporate      
Restructuring Cost and Reserve [Line Items]      
Restructuring Costs 25.2 $ 0.0  
Other Restructuring Plans      
Restructuring Cost and Reserve [Line Items]      
Beginning balance 1.5    
Restructuring Costs 0.0    
Amounts Paid (0.3)    
Ending balance 1.2   $ 1.5
Severance and Employee-Related | Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Beginning balance 0.0    
Restructuring Costs 30.5    
Amounts Paid (14.9)    
Non-cash costs (10.4)    
Ending balance 5.2   0.0
Severance and Employee-Related | Other Restructuring Plans      
Restructuring Cost and Reserve [Line Items]      
Beginning balance 0.9    
Restructuring Costs 0.0    
Amounts Paid (0.3)    
Ending balance 0.6   0.9
Severance and Employee-Related | May 2020 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Beginning balance 1.0    
Restructuring Costs 0.0   3.4
Amounts Paid (0.5)    
Ending balance 0.5   1.0
Exit or Disposal Activities | Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Beginning balance 0.0    
Restructuring Costs 0.0    
Amounts Paid 0.0    
Non-cash costs 0.0    
Ending balance 0.0   0.0
Exit or Disposal Activities | Other Restructuring Plans      
Restructuring Cost and Reserve [Line Items]      
Beginning balance 0.6    
Restructuring Costs 0.0    
Amounts Paid 0.0    
Ending balance 0.6   0.6
Total | Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Beginning balance 0.0    
Restructuring Costs 30.5    
Amounts Paid (14.9)    
Non-cash costs (10.4)    
Ending balance $ 5.2   $ 0.0