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Employee Benefit Plans - Schedule of Funded Status and Amounts Recognized in the Balance Sheet (Details) - USD ($)
$ in Millions
 12 Months Ended
Jun. 03, 2023
May 28, 2022
May 29, 2021
Components of the amounts recognized in the Consolidated Balance Sheets:      
Pension and post-retirement benefits $ 7.5 $ 25.0  
United States | Pension Plan      
Change in benefit obligation:      
Benefit obligation at beginning of year 152.6 0.0  
Acquisition of Knoll 0.0 189.8  
Interest cost 6.1 3.9 $ 0.0
Expected Administrative Expenses 0.6 0.5 0.0
Loss related to settlement 4.7 1.0  
Foreign exchange impact 0.0 0.0  
Actuarial gain (loss) (18.2) (28.0)  
Administrative expenses paid (0.7) (0.5)  
Benefits paid (7.2) (4.2)  
Benefits paid related to settlement (14.1) (9.9)  
Benefit obligation at end of year 123.8 152.6 0.0
Change in plan assets:      
Fair value of plan assets at beginning of year 144.0 0.0  
Acquisition of Knoll 0.0 175.4  
Actual return on plan assets (2.9) (16.8)  
Foreign exchange impact 0.0  
Employer contributions 7.2 0.0  
Actual expenses paid (0.7) (0.5)  
Benefits paid (21.3) (14.1)  
Fair value of plan assets at end of year 126.3 144.0 0.0
Funded status:      
Over (under) funded status at end of year 2.5 (8.6)  
Components of the amounts recognized in the Consolidated Balance Sheets:      
Current assets 0.0 0.0  
Non-current assets 2.5 0.0  
Current liabilities 0.0 0.0  
Pension and post-retirement benefits 0.0 8.6  
Components of the amounts recognized in Accumulated other comprehensive loss before the effect of income taxes:      
Prior service cost 0.0 0.0  
Unrecognized net actuarial (gain) loss (4.4) (2.8)  
Accumulated other comprehensive (gain) loss (4.4) (2.8)  
International      
Change in benefit obligation:      
Expected Administrative Expenses   0.0  
Loss related to settlement   0.0  
Administrative expenses paid   0.0  
Benefits paid related to settlement   0.0  
International | Pension Plan      
Change in benefit obligation:      
Benefit obligation at beginning of year 104.5 140.9  
Acquisition of Knoll 0.0 0.0  
Interest cost 3.1 2.4 2.2
Expected Administrative Expenses 0.0 0.0 0.0
Loss related to settlement 0.0    
Foreign exchange impact (2.5) (14.1)  
Actuarial gain (loss) (26.2) (21.9)  
Administrative expenses paid 0.0    
Benefits paid (2.9) (2.8)  
Benefits paid related to settlement 0.0    
Benefit obligation at end of year 76.0 104.5 140.9
Change in plan assets:      
Fair value of plan assets at beginning of year 93.5 109.9  
Acquisition of Knoll 0.0 0.0  
Actual return on plan assets (9.1) (6.9)  
Foreign exchange impact (1.6) (11.8)  
Employer contributions 4.5 5.0  
Actual expenses paid 0.0 0.0  
Benefits paid (2.9) (2.7)  
Fair value of plan assets at end of year 84.4 93.5 $ 109.9
Funded status:      
Over (under) funded status at end of year 8.4 (11.0)  
Components of the amounts recognized in the Consolidated Balance Sheets:      
Current assets 0.0 0.0  
Non-current assets 8.4 0.0  
Current liabilities 0.0 0.0  
Pension and post-retirement benefits 0.0 10.9  
Components of the amounts recognized in Accumulated other comprehensive loss before the effect of income taxes:      
Prior service cost 0.4 0.5  
Unrecognized net actuarial (gain) loss 25.7 41.4  
Accumulated other comprehensive (gain) loss $ 26.1 $ 41.9