Revenue from Contracts with Customers - Revenue Disaggregated By Product Type And Reportable Segment (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Mar. 02, 2024	Mar. 04, 2023	Mar. 02, 2024	Mar. 04, 2023
Disaggregation of Revenue [Line Items]
Net sales	$ 872.3	$ 984.7	$ 2,739.5	$ 3,130.4
Americas Contract | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	441.1	484.6	1,407.6	1,551.7
Americas Contract | Workplace | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	281.8	313.5	917.3	994.3
Americas Contract | Performance Seating | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	96.3	102.8	303.4	336.7
Americas Contract | Lifestyle | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	55.3	60.8	171.9	200.3
Americas Contract | Other | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	7.7	7.5	15.0	20.4
International Contract & Specialty | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	217.3	242.5	686.8	779.9
International Contract & Specialty | Workplace | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	34.8	37.5	110.0	131.4
International Contract & Specialty | Performance Seating | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	55.8	63.3	172.7	197.9
International Contract & Specialty | Lifestyle | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	81.5	92.4	258.8	299.0
International Contract & Specialty | Other | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	45.2	49.3	145.3	151.6
Global Retail | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	213.9	257.6	645.1	798.8
Global Retail | Workplace | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	3.3	20.3	10.8	69.7
Global Retail | Performance Seating | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	50.4	59.8	148.1	161.9
Global Retail | Lifestyle | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	159.9	177.2	485.3	565.8
Global Retail | Other | Operating Segments
Disaggregation of Revenue [Line Items]
Net sales	$ 0.3	$ 0.3	$ 0.9	$ 1.4