Revenue from Contracts with Customers - Revenue Disaggregated By Product Type And Reportable Segment (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Dec. 02, 2023	Dec. 03, 2022	Dec. 02, 2023	Dec. 03, 2022
Disaggregation of Revenue [Line Items]
Net sales	$ 949.5	$ 1,066.9	$ 1,867.2	$ 2,145.7
Americas Contract | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	476.1	529.7	966.5	1,067.1
Americas Contract | Workplace | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	311.3	342.1	635.5	680.8
Americas Contract | Performance Seating | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	103.8	115.0	207.1	233.9
Americas Contract | Lifestyle | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	56.0	68.4	116.6	139.5
Americas Contract | Other | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	5.0	4.2	7.3	12.9
International Contract & Specialty | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	241.2	264.9	469.5	537.4
International Contract & Specialty | Workplace | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	36.5	49.5	75.2	93.8
International Contract & Specialty | Performance Seating | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	64.3	65.7	116.9	134.7
International Contract & Specialty | Lifestyle | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	88.9	99.6	177.3	206.6
International Contract & Specialty | Other | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	51.5	50.1	100.1	102.3
Global Retail | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	232.2	272.3	431.2	541.2
Global Retail | Workplace | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	3.3	21.9	7.5	49.4
Global Retail | Performance Seating | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	55.6	50.9	97.7	102.1
Global Retail | Lifestyle | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	172.9	198.8	325.4	388.6
Global Retail | Other | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	$ 0.4	$ 0.7	$ 0.6	$ 1.1