Rangevoting.org had the interesting idea of trying to promote a non-FPTP system (in their case, range voting, obviously :P ) by convincing the major parties to

Rangevoting.org had the interesting idea of trying to promote a non-FPTP system (in their case, range voting, obviously :P ) by convincing the major parties to use it in their primaries/caucauses. The idea I think being that using it for internal elections is something they (for now) stand to gain from, and since those are often truly multi-way contests there's no internal equivalents of the "major parties" who would (know that they could) benefit in the primaries from sticking to FPTP. I don't think they're really active anymore, but it remains the most plausible approach I've heard.