Suppose the U.S. House of Representatives' 435 seats are narrowly divided something like 220-215 between the two major parties. Normally, the majority party chooses the Speaker of the House.
But suppose the majority party has three candidates for speaker, A, B, and C, and the minority party prefers one of them. Can the minority party then back one of the three candidates from the other party giving him or her the needed majority, when the majority party can't agree among itself? Conversely, has there ever been a situation in history where (in the above example) three members of Congress defected from the majority and helped elect a House speaker from the minority party?
Or is it the case where only the majority party gets to elect a speaker, even when the person commands only a plurality of the vote?