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Restructuring and Integration Expense - Schedule of Restructuring Expenses by Segment (Details) - USD ($)
 3 Months Ended 9 Months Ended
Mar. 01, 2025
Mar. 02, 2024
Mar. 01, 2025
Mar. 02, 2024
Restructuring Cost and Reserve [Line Items]        
Restructuring expense $ 4,200,000 $ 1,700,000 $ 4,200,000 $ 8,700,000
North America Contract        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 2,400,000 1,500,000 2,400,000 6,100,000
International Contract        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 1,700,000 100,000 1,700,000 1,300,000
Global Retail        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 100,000 100,000 100,000 1,300,000
Knoll Integration        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 0 7,600,000 28,300,000 18,400,000
Knoll Integration | Corporate        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 0 0 0 100,000
Knoll Integration | North America Contract | Operating Segments        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 0 7,600,000 24,800,000 18,100,000
Knoll Integration | International Contract | Operating Segments        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 0 0 3,200,000 200,000
Knoll Integration | Global Retail | Operating Segments        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense $ 0 $ 0 $ 300,000 $ 0