The rule changes under discussion start with a proposal to force those seeking new positions in the House GOP leadership to give up their current positions in order to run. That would currently affect Majority Leader Kevin O. McCarthy (Calif.), who is seeking to succeed outgoing Speaker John A. Boehner (Ohio), and Majority Whip Steve Scalise (La.), who is seeking to replace McCarthy should his speaker bid succeed.

But the proposed changes extend to measures intended to enhance party unity. Some hard-line conservatives have floated changes that would devolve power from the elected leadership and powerful committee chairs to more junior, rank-and-file members by seeking to enforce “regular order” — an ill-defined but much-invoked concept of allowing legislation to bubble up organically through committees to the floor rather than through the more assertive top-down agenda-setting that has come to be everyday practice in the House.

First-term Rep. Dave Brat (R-Va.), for instance, has proposed codifying the heretofore informal “Hastert Rule” holding that only measures supported by a majority of the Republican House majority be brought forth for floor consideration. For instance, the stopgap funding bill that passed Wednesday, averting a government shutdown, failed that test, with 151 of 247 Republicans opposing it.