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Significant Accounting and Reporting Policies - Goodwill and Indefinite-lived Intangible Assets (Details)
$ in Millions
 3 Months Ended 9 Months Ended 12 Months Ended
May 31, 2025
USD ($)
reportingUnit
Mar. 01, 2025
USD ($)
Mar. 01, 2025
USD ($)
May 31, 2025
USD ($)
Jun. 01, 2024
USD ($)
Jun. 03, 2023
USD ($)
Indefinite-lived Intangible Assets [Line Items]            
Goodwill $ 1,152.4     $ 1,152.4 $ 1,226.3 $ 1,221.7
Number of reporting units | reportingUnit 4          
Impairment charges       $ 37.7 16.8  
Trade name            
Indefinite-lived Intangible Assets [Line Items]            
Impairment charges   $ 37.7        
Knoll Trade Name            
Indefinite-lived Intangible Assets [Line Items]            
Impairment charges         8.9 19.7
Impairment, Intangible Asset, Indefinite-Lived (Excluding Goodwill), Statement of Income or Comprehensive Income [Extensible Enumeration]       Impairment charges    
Muuto Trade Name            
Indefinite-lived Intangible Assets [Line Items]            
Impairment charges         7.9  
Impairment, Intangible Asset, Indefinite-Lived (Excluding Goodwill), Statement of Income or Comprehensive Income [Extensible Enumeration]       Impairment charges    
Valuation Relief From Forecast Growth Rate 10% Decrease | Knoll Trade Name            
Indefinite-lived Intangible Assets [Line Items]            
Impairment charges       $ 12.0    
Measurement inputs (as percent)       10.00%    
Valuation Relief From Forecast Growth Rate 10% Decrease | Muuto Trade Name            
Indefinite-lived Intangible Assets [Line Items]            
Impairment charges       $ 7.0    
Measurement inputs (as percent)       10.00%    
Royalty Rate | Valuation Approach Royalty Rate 25bps Decrease | Knoll Trade Name            
Indefinite-lived Intangible Assets [Line Items]            
Impairment charges       $ 15.0    
Measurement inputs (as percent)       0.25%    
Royalty Rate | Valuation Approach Royalty Rate 25bps Decrease | Muuto Trade Name            
Indefinite-lived Intangible Assets [Line Items]            
Impairment charges       $ 4.0    
Measurement inputs (as percent)       0.25%    
Royalty Rate | Valuation Approach Discount Rate 100bps Increase | Knoll Trade Name            
Indefinite-lived Intangible Assets [Line Items]            
Impairment charges       $ 11.0    
Measurement inputs (as percent)       1.00%    
Royalty Rate | Valuation Approach Discount Rate 100bps Increase | Muuto Trade Name            
Indefinite-lived Intangible Assets [Line Items]            
Impairment charges       $ 6.0    
Measurement inputs (as percent)       1.00%    
Minimum | Discount Rate            
Indefinite-lived Intangible Assets [Line Items]            
Goodwill, measurement input (as percent)     12.00%      
Intangible asset, measurement input (as percent)   12.80%        
Minimum | Long-term Growth Rate            
Indefinite-lived Intangible Assets [Line Items]            
Goodwill, measurement input (as percent)     2.50%      
Intangible asset, measurement input (as percent)   2.50%        
Minimum | Royalty Rate            
Indefinite-lived Intangible Assets [Line Items]            
Intangible asset, measurement input (as percent)   1.00%        
Maximum | Discount Rate            
Indefinite-lived Intangible Assets [Line Items]            
Goodwill, measurement input (as percent)     15.00%      
Intangible asset, measurement input (as percent)   17.30%        
Maximum | Long-term Growth Rate            
Indefinite-lived Intangible Assets [Line Items]            
Goodwill, measurement input (as percent)     3.00%      
Intangible asset, measurement input (as percent)   3.00%        
Maximum | Royalty Rate            
Indefinite-lived Intangible Assets [Line Items]            
Intangible asset, measurement input (as percent)   3.00%        
North America Contract            
Indefinite-lived Intangible Assets [Line Items]            
Reporting unit, percentage of fair value in excess of carrying amount (percent)   32.00% 32.00%      
International Contract            
Indefinite-lived Intangible Assets [Line Items]            
Goodwill $ 159.1     $ 159.1 $ 154.0 $ 153.1
Reporting unit, percentage of fair value in excess of carrying amount (percent)   63.00% 63.00%      
Coverings Reporting Units            
Indefinite-lived Intangible Assets [Line Items]            
Reporting unit, percentage of fair value in excess of carrying amount (percent)   10.00% 10.00%      
Global Retail            
Indefinite-lived Intangible Assets [Line Items]            
Goodwill impairment   $ 30.1        
Goodwill   357.0 $ 357.0      
Holly Hunt            
Indefinite-lived Intangible Assets [Line Items]            
Goodwill impairment   62.2        
Goodwill   33.0 33.0      
Goodwill transfers in (out)     (33.0)      
Coverings Reporting Units | Pro Forma            
Indefinite-lived Intangible Assets [Line Items]            
Goodwill impairment   $ 3.0        
North America Contract            
Indefinite-lived Intangible Assets [Line Items]            
Goodwill transfers in (out)     (26.1)      
International Contract Reporting Unit            
Indefinite-lived Intangible Assets [Line Items]            
Goodwill transfers in (out)     26.1      
Global Retail Reporting Unit            
Indefinite-lived Intangible Assets [Line Items]            
Goodwill transfers in (out)     $ 33.0