Really not sure how that would be possible. The Republican party is fairly evenly split between corporate/Reaganesque Republicans and the populist right. There are no other power blocs that could enact the kind of steering you're hoping for. Even electoral defeat doesnt seem to phase them much (they're all voting against popular progressive bills in lockstep).

The best we could probably hope for is that those two wings of the party turn on each other but as Trump demonstrated they seem to be able to find enough common ground to work together.