That would be nice, but the presidential electoral setup all but forbids this from happening. Setting aside structural barriers such as ballot access restrictions, the U.S. uses a winner-take-all, first-past-the-post election system, where once a presidential candidate beats all their opponents by at least a single vote within a state, they are awarded 100% of all the votes in that state that ultimately matter. This discourages voters who might otherwise be inclined to vote for a third party from doing so because of the concept of wasting the vote on someone who's destined to lose (something that also happens, BTW, when your major party presidential candidate loses your state anyway.) There's also the general tendency of countries that have single-member districts, instead of proportional representation, to emerge as two-party countries. Both the US and UK are emblematic of that.
If we truly want more than two strong parties, we would probably need to move from a winner-take-all system to a proportional representation system, at minimum. Almost none of us here will ever live to see that happen.