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Acquisitions and Dispositions - Narrative (Details) - USD ($) $ in Thousands |  |  |  |  |  | 3 Months Ended | 11 Months Ended | 12 Months Ended |
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Jul. 03, 2023 | Dec. 07, 2021 | Sep. 02, 2021 | Jul. 28, 2021 | Jan. 29, 2021 | Sep. 30, 2023 | Sep. 24, 2022 | Dec. 06, 2021 | Dec. 30, 2023 | Dec. 31, 2022 | Dec. 25, 2021 | Oct. 25, 2021
Disposal Group, Disposed of by Means Other than Sale, Not Discontinued Operations, Exchange | Heatlink Group, Inc. |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Ownership interest transferred (as a percent) | 100.00% |  |  |  |  |  |  |  |  |  |  |
Net sales of disposed of business |  |  |  |  |  |  |  |  | $ 15,600 | $ 39,100 |  |
Operating income of disposed business |  |  |  |  |  |  |  |  | $ 1,700 | 7,200 |  |
Consideration for sale of businesses | $ 26,000 |  |  |  |  |  |  |  |  |  |  |
Gain (loss) on disposal of businesses |  |  |  |  |  | $ 4,100 |  |  |  |  |  |
Disposal Group, Disposed of by Sale, Not Discontinued Operations | Die-Mold |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Net sales of disposed of business |  |  |  |  |  |  |  |  |  |  | $ 10,900 |
Consideration for sale of businesses |  |  | $ 22,800 |  |  |  |  |  |  |  |  |
Net income of disposed business |  |  |  |  |  |  |  |  |  | $ 2,200 |  |
Gain (loss) on disposal of businesses |  |  | $ 4,700 |  |  |  |  |  |  |  |  |
Disposal Group, Disposed of by Sale, Not Discontinued Operations | Copper Bar |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Consideration for sale of businesses |  |  |  |  |  |  |  |  |  |  |  | $ 10,100
Assets |  |  |  |  |  |  |  |  |  |  |  | $ 3,600
Gain (loss) on disposal of businesses |  |  |  |  |  |  |  |  |  |  | 6,500 |
Disposal Group, Disposed of by Sale, Not Discontinued Operations | Fabricated Tube Products and Shoals Tubular, Inc. |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Net sales of disposed of business |  |  |  |  |  |  |  |  |  |  | 37,000 |
Consideration for sale of businesses |  |  |  | $ 75,700 |  |  |  |  |  |  |  |
Assets |  |  |  | 32,700 |  |  |  |  |  |  |  |
Net income of disposed business |  |  |  |  |  |  |  |  |  |  | $ 5,500 |
Carrying value of the liabilities disposed |  |  |  | 3,600 |  |  |  |  |  |  |  |
Gain (loss) on disposal of businesses |  |  |  | $ 46,600 |  |  |  |  |  |  |  |
Mueller Middle East |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Ownership interest acquired (as a percent) |  | 55.00% |  |  |  |  |  |  |  |  |  |
Total consideration paid |  | $ 20,017 |  |  |  |  |  |  |  |  |  |
Cash paid for acquisition |  | 15,800 |  |  |  |  |  |  |  |  |  |
Debt assumed |  | 2,600 |  |  |  |  |  |  |  |  |  |
Payment for contingent consideration liability |  | 1,000 |  |  |  |  |  |  |  |  |  |
Equity interest issued or issuable |  | $ 700 |  |  |  |  |  |  |  |  |  |
Asset acquisition, pro forma revenue from acquiree |  |  |  |  |  |  |  | $ 48,200 |  |  |  |
Hart & Cooley Flexible Duct Business |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Total consideration paid |  |  |  |  | $ 15,300 |  |  |  |  |  |  |
Cash paid for acquisition |  |  |  |  | $ 14,000 |  |  |  |  |  |  |
Payment for contingent consideration liability |  |  |  |  |  |  | $ 1,300 |  |  |  |  |
Retail Distribution Business |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Ownership interest acquired (as a percent) | 11.00% |  | 28.00% |  |  |  |  |  |  |  | 17.00% |
Retail Distribution Business | Die-Mold |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Ownership interest acquired (as a percent) |  |  | 17.00% |  |  |  |  |  |  |  |  |
Mueller Middle East |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Interest in the joint venture, ownership percentage |  | 15.00% |  |  |  |  |  |  |  |  |  |
Mueller Middle East | Joint Venture |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Interest in the joint venture, ownership percentage |  | 40.00% |  |  |  |  |  |  |  |  |  |

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