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Restructuring and Integration Expense - Summary of Restructuring Expenses by Segment (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
Mar. 02, 2024
Mar. 04, 2023
Mar. 02, 2024
Mar. 04, 2023
Restructuring Cost and Reserve [Line Items]        
Restructuring expense $ 1.7 $ 4.6 $ 8.7 $ 19.8
Americas Contract        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 1.5 4.4 5.8 17.5
International Contract & Specialty        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 0.1 0.0 1.6 0.7
Global Retail        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 0.1 0.2 1.3 1.6
Knoll Integration        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 7.6 4.0 18.4 12.7
Knoll Integration | Corporate        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 0.0 1.3 0.1 4.3
Knoll Integration | Americas Contract | Operating Segments        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 5.8 2.2 15.3 6.2
Knoll Integration | International Contract & Specialty | Operating Segments        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 1.8 0.5 3.0 2.0
Knoll Integration | Global Retail | Operating Segments        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense $ 0.0 $ 0.0 $ 0.0 $ 0.2