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Restructuring and Integration Expense - Summary of Restructuring Expenses by Segment (Details) - USD ($)
$ in Millions
 3 Months Ended 6 Months Ended
Dec. 02, 2023
Dec. 03, 2022
Dec. 02, 2023
Dec. 03, 2022
Restructuring Cost and Reserve [Line Items]        
Restructuring expense $ 1.8 $ 14.7 $ 7.0 $ 15.2
Americas Contract        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 0.0 13.2 4.3 13.2
International Contract & Specialty        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 0.8 0.7 1.5 0.7
Global Retail        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 1.0 0.8 1.2 1.3
Knoll Integration        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 6.9 4.1 10.8 8.7
Knoll Integration | Corporate        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 0.0 2.0 0.1 3.0
Knoll Integration | Americas Contract | Operating Segments        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 6.4 1.1 9.5 4.0
Knoll Integration | International Contract & Specialty | Operating Segments        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense 0.5 1.0 1.2 1.5
Knoll Integration | Global Retail | Operating Segments        
Restructuring Cost and Reserve [Line Items]        
Restructuring expense $ 0.0 $ 0.0 $ 0.0 $ 0.2