They could solve the House of Representatives problem with a single vote if they used ranked choice voting. Here's how it would work:
All members are given a list of all possible candidates.
Anyone willing to be considered is on the list. The Democrats could nominate some additional choices after Jeffries if they want. Both parties could nominate members of the opposite party they consider more acceptable than those that other party put forward itself.
They'd have to vote in favor of using ranked-choice voting, and given the short-wit attention seekers making up half the House, that prospect strikes me as a bit unlikely.
Maybe next November when droves of them get voted out. We shall see.
@AlphaCentauri
Okay, it's not possible.