Significant Accounting and Reporting Policies - Schedule of Goodwill and Other Indefinite-lived Intangible Assets (Details) - USD ($) $ in Millions	12 Months Ended
Jun. 01, 2024	Jun. 03, 2023	May 28, 2022
Goodwill [Roll Forward]
Goodwill	$ 1,347.2	$ 1,351.7	$ 489.7
Sale of owned dealer			(0.3)
Acquisition of Knoll			903.5
Foreign currency translation adjustments	4.6	(4.5)	(41.2)
Accumulated impairment losses	(125.5)	(125.5)	(125.5)
Net goodwill	1,226.3	1,221.7	1,226.2
Indefinite-lived Intangible Assets [Roll Forward]
Beginning balance	480.7	501.0
Foreign currency translation adjustments	1.6	(0.6)
Acquisition of Knoll		(19.7)
Impairment charges	(16.8)
Ending balance	465.5	480.7	501.0
Americas Contract
Goodwill [Roll Forward]
Goodwill	565.1	566.8	197.4
Sale of owned dealer			(0.3)
Acquisition of Knoll			346.0
Foreign currency translation adjustments	1.7	(1.7)	23.7
Accumulated impairment losses	(36.7)	(36.7)	(36.7)
Net goodwill	530.1	528.4	530.1
International Contract & Specialty
Goodwill [Roll Forward]
Goodwill	303.0	304.3	111.2
Sale of owned dealer			0.0
Acquisition of Knoll			226.8
Foreign currency translation adjustments	1.4	(1.3)	(33.7)
Accumulated impairment losses	0.0	0.0	0.0
Net goodwill	304.4	303.0	304.3
Global Retail
Goodwill [Roll Forward]
Goodwill	479.1	480.6	181.1
Sale of owned dealer			0.0
Acquisition of Knoll			330.7
Foreign currency translation adjustments	1.5	(1.5)	(31.2)
Accumulated impairment losses	(88.8)	(88.8)	(88.8)
Net goodwill	$ 391.8	$ 390.3	$ 391.8

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