In 1860, the Republican party was a new party which won!
A new party could win but the trick is to paint the Dems and Pubs as one party in the minds of the voters. Seeing the behaviors of both parties, I’m convinced they are one party!
It won because of a 4-way split, but Republicans essentially supplanted the Whigs, which disintegrated after the 1854 elections, and assimilated the briefly-existing Know-Nothings. Even a decent chunk of Conservatives walked out of the GOP, the GOP would still exist, and in a lot of places, if the GOP & Conservatives ran candidates, the Democrats would benefit enormously. Only if the GOP completely disintegrated would a “new” rightist party benefit.