Under the plan, the ability of one representative to essentially force a vote of no confidence in the speaker would be eliminated. That threat from members of the House Freedom Caucus led to the resignation of Speaker John A. Boehner in 2015 and is seen as a way that just a few members can handcuff the speaker.

Instead, the so-called motion to vacate the chair would be replaced by a process in which one-third of the House would have to publicly sign a petition to force such a vote.

The rules proposal was drafted over months of negotiation among the 48 members of the Problem Solvers Caucus, which is equally split between Republicans and Democrats. It would institute new standards for the automatic consideration of legislation with strong bipartisan support. The authors believe the plan, which has the backing of at least 75 percent of the group’s membership, would foster more bipartisanship and incite debate on major issues that are being sidelined by political considerations.