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Restructuring and Integration Expense - Summary of Restructuring Expenses by Segment (Details) - USD ($)
$ in Millions
 3 Months Ended 12 Months Ended
Sep. 02, 2023
Sep. 03, 2022
Jun. 03, 2023
Restructuring Cost and Reserve [Line Items]      
Restructuring expense $ 5.2 $ 0.5  
Americas Contract      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense 4.3 0.0  
International Contract & Specialty      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense 0.7 0.0  
Retail      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense 0.2 0.5  
Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense 3.9 4.6  
Knoll Integration | Corporate      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense 0.1 1.0  
Knoll Integration | Americas Contract | Operating Segments      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense 3.1 2.9  
Knoll Integration | International Contract & Specialty | Operating Segments      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense 0.7 0.5  
Knoll Integration | Retail | Operating Segments      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense $ 0.0 $ 0.2  
2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense     $ 34.0