The third party. And if the Democrats and Republicans ever want to be viable again, they'll have to join with each other or with the 3rd party, depending on which is closer ideologically. So we're back to 2 parties.
And by the way, support for any 3rd parties in the US is currently at less than 5%, nowhere close to the >50‰ required to make this scenario plausible. It has happened before, though not in the last 150 years, usually with the total collapse of one of the two parties. Andrew Jackson personally caused the collapse of the existing parties by basically turning them into pro-Jackson and anti-Jackson parties. And then a few decades later the anti-Jackson party itself completely split over the question of slavery, and then the Civil War created the two parties we have today, Democrats and Republicans. The two parties almost completely swapped supporters and positions in the 1960s due to Nixon's "Southern Strategy", but the two ideological groups of voters have been the same since the mid-1800s even though they've changed names.
Most US elections, in particular the Presidential one, are first past the post and winner take all. There's no coalitions or anything. Only one party can win. If the Democrats, for example, split into a Moderates and a Progressives party, the election landscape will go from this:
Democrats ~50%
Republicans ~50%
To this:
Moderates ~30%
Progressives ~20%
Republicans ~50%
And Republicans are guaranteed a win. The Republicans don't win 50% of the government, they get the whole government. Progressives and Moderates get nothing. The only possible way to defeat the Republicans is by combining the Progressives and Moderates into a single party.
This whole "I'll just pretend that you admitted to the thing I accused you of" gaslighting thing is way too obviously a ploy to distract from your complete failure of an argument.
Speaking as a blue state taxpayer, I'd rather we give them whatever remedial education they need instead of turning them away.