Stock-Based Compensation - Schedule of Restricted Stock Unit (RSU) Activity (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
May 31, 2025	Jun. 01, 2024	Jun. 03, 2023
Restricted stock units
Share-based Compensation Arrangements by Share-based Payment Award [Roll Forward]
Beginning balance (in shares)	930,647
Granted (in shares)	1,054,335
Forfeited (in shares)	(75,878)
Released (in shares)	(337,906)
Ending balance (in shares)	1,571,198	930,647
Weighted Average Grant-Date Fair Value
Outstanding, at beginning of year (in dollar per share)	$ 21.92
Granted (in dollar per share)	28.24	$ 17.30	$ 27.76
Forfeited (in usd per share)	22.60
Released (in usd per share)	26.02
Outstanding, at end of year (in dollar per share)	$ 25.22	$ 21.92
Aggregate Intrinsic Value
Aggregate intrinsic value (in millions)	$ 26.7	$ 25.9
Weighted-Average Remaining Contractual Term
Weighted average remaining contractual term (years)	8 months 12 days	1 year 2 months 12 days
Restricted stock awards
Share-based Compensation Arrangements by Share-based Payment Award [Roll Forward]
Granted (in shares)	0	0	0

Share-Based Compensation Arrangement by Share-Based Payment Award, Non-Option Equity Instruments, Released in Period

No definition available.

Name:	mlkn_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsReleasedInPeriod
Namespace Prefix:	mlkn_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Share-based Compensation Arrangements By Share-based Payment Award, Equity Instruments Other than Options, Released In Period, Weighted Average Grant Date Fair Value

+ References

No definition available.

+ Details

Name:	mlkn_ShareBasedCompensationArrangementsByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReleasedInPeriodWeightedAverageGrantDateFairValue
Namespace Prefix:	mlkn_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsAdditionalDisclosuresAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of equity-based payment instruments, excluding stock (or unit) options, that were forfeited during the reporting period.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average fair value as of the grant date of equity-based award plans other than stock (unit) option plans that were not exercised or put into effect as a result of the occurrence of a terminating event.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The weighted average fair value at grant date for nonvested equity-based awards issued during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of non-vested equity-based payment instruments, excluding stock (or unit) options, that validly exist and are outstanding as of the balance sheet date.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(ii)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Per share or unit weighted-average fair value of nonvested award under share-based payment arrangement. Excludes share and unit options.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average remaining contractual term for equity-based awards excluding options, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 718
-SubTopic 10
-Subparagraph (e)(1)
-Name Accounting Standards Codification
-Paragraph 2
-Section 50
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsOutstandingWeightedAverageRemainingContractualTerms
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

Name:	us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Intrinsic value of nonvested award under share-based payment arrangement. Excludes share and unit options.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-4

+ Details

Name:	us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueNonvested
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_RestrictedStockUnitsRSUMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_RestrictedStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: