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Restructuring and Integration Expense - Additional Information (Details) - USD ($)
 3 Months Ended 12 Months Ended
Sep. 02, 2023
Sep. 03, 2022
Jun. 03, 2023
Restructuring Cost and Reserve [Line Items]      
Restructuring expense $ 5,200,000 $ 500,000  
Knoll Integration      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense 3,900,000 4,600,000  
Knoll Integration | Exit and Disposal Activities      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense 3,400,000    
Knoll Integration | Other Restructuring      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense 500,000 2,000,000  
Knoll Integration | Severance and Employee Benefit      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense 0 1,200,000  
Knoll Integration | Lease Termination Costs      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense   $ 1,400,000  
Knoll Integration | Knoll      
Restructuring Cost and Reserve [Line Items]      
Restructuring and related cost, expected cost 150,000,000    
2023 Restructuring Plan      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense     $ 34,000,000
Restructuring costs expected 0    
2023 Restructuring Plan | Severance and Employee Benefit      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense 0   27,900,000
2023 Restructuring Plan | Severance and Employee Benefit | Minimum      
Restructuring Cost and Reserve [Line Items]      
Cost savings     30,000,000
2023 Restructuring Plan | Severance and Employee Benefit | Maximum      
Restructuring Cost and Reserve [Line Items]      
Cost savings     35,000,000
2023 Restructuring Plan | Non-Cash Asset Impairments      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense     $ 6,100,000
2024 Restructuring Plan | Minimum      
Restructuring Cost and Reserve [Line Items]      
Annualized expense reduction 5,000,000    
2024 Restructuring Plan | Maximum      
Restructuring Cost and Reserve [Line Items]      
Annualized expense reduction 6,000,000    
2024 Restructuring Plan | Severance and Employee Benefit      
Restructuring Cost and Reserve [Line Items]      
Restructuring expense $ 5,200,000