Fourteen House Democrats are vowing to withhold their votes for Speaker unless the candidate agrees to overhaul House rules, according to an analysis by The Hill.

The list of lawmakers includes 10 Democrats who previously made such a pledge, as well as four congressional candidates who made a similar promise on the campaign trail and won their race on Tuesday.

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With Democrats likely to have somewhere around a 20- to 25-seat majority next year, the group is poised to hold some sway over the selection of the next Speaker. House Minority Leader Nancy Pelosi Nancy PelosiPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare House lawmakers reach deal to avert shutdown Centrist Democrats 'strongly considering' discharge petition on GOP PPP bill MORE (D-Calif.), the likely front-runner to lead the caucus, has reviewed the proposal and is open to making some changes.

The push for rule changes appears to have near-universal support in the conference, with centrist Blue Dog Democrats also calling for an overhaul.

“She has to be inclusive … of the more moderate folks,” Rep. Henry Cuellar (D-Texas), a leader of the conservative-leaning Blue Dogs, said Tuesday night.

There are also seven Republicans who won reelection and vowed to trade Speaker votes for an overhaul of the House rules.

Rep. Tom Reed Thomas (Tom) W. ReedCentrist House group offers bipartisan COVID-19 relief deal House approves two child care bills aimed at pandemic Diabetes Caucus co-chairs say telehealth expansion to continue beyond pandemic MORE (R-N.Y.), co-chair of the bipartisan Problem Solvers Caucus, said he would consider supporting a Democratic Speaker if that candidate agreed to the package. Leaders of the caucus have been working for months to get lawmakers on board with the effort, which they say is an attempt to “break the gridlock” in Washington.

Their proposal includes giving fast-track consideration to any bill with widespread support, making it easier to add amendments to legislation and making it harder for a small group of rebellious lawmakers to oust the Speaker.

The package also would grant members a markup on one piece of legislation per session if it has a co-sponsor from the opposite party, as well as mandate a joint bipartisan meeting at the beginning of every Congress.

The suggested changes are designed to redistribute power, which reform advocates argue is too concentrated at the top, and empower more rank-and-file members in both parties.

The proposal has picked up some steam in recent months, especially as lawmakers grow increasingly frustrated with the gridlock and polarization in Congress.

The 14 Democrats who have made the pledge thus far are Reps. Josh Gottheimer Joshua (Josh) GottheimerCentrist House group offers bipartisan COVID-19 relief deal Hillicon Valley: Lawmakers introduce resolution condemning QAnon | US Cyber Command leader vows to 'defend forward' in protecting nation from cyberattacks House Democrats request briefing on seizure of terrorist cryptocurrency assets MORE (N.J.), Jim Costa James (Jim) Manuel CostaHouse Democrats call on State Department for information on Uighur prisoner Ekpar Asat Hispanic Caucus requests meeting with private detention center CEOs Black Caucus rallies behind Meeks for Foreign Affairs gavel MORE (Calif.), Tom O'Halleran (Ariz.), Kurt Schrader Walter (Kurt) Kurt SchraderHouse members race to prepare for first-ever remote votes The 14 Democrats who broke with their party on coronavirus relief vote House votes to condemn Trump Medicaid block grant policy MORE (Ore.), Tom Suozzi (N.Y.), Salud Carbajal Salud CarbajalNunes opponent pins hopes on shifting demographics in uphill battle Democratic lawmakers launch 'Mean Girls'-inspired initiative to promote face masks Federal employees push for COVID-19 protections in 'dangerous' workplaces MORE (Calif.), Dan Lipinski (Ill.), Stephanie Murphy Stephanie MurphyDemocrats scramble on COVID-19 relief amid division, Trump surprise Bank lobbying group launches ad backing Collins reelection bid House Democrats call on State Department for information on Uighur prisoner Ekpar Asat MORE (Fla.), Vicente González (Texas) and Darren Soto Darren Michael SotoFlorida Democrat introduces bill to recognize Puerto Rico statehood referendum Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status Let's build a better post-COVID future than fossil fuel consolidation MORE (Fla.), as well as Rep.-elects Susie Lee (Nev.), Jeff Van Drew (N.J.), Ann Kirkpatrick Ann KirkpatrickArizona Rep. Tom O'Halleran wins Democratic primary Arizona Rep. Ann Kirkpatrick wins Democratic primary Cook shifts 20 House districts toward Democrats MORE (Ariz.) and Dean Phillips (Minn.).

--Mike Lillis contributed