Yeah, that’s about right. Plus then you had the factions with the Jacksonian Democrats and Whigs on the issue of slavery, which necessitated the collapse of one of those parties as a result (the Dems could’ve also, only because the Whigs were weaker by the 1850s).
I forgot if it was Madison or Monroe (I think Monroe) who was moving in the direct of the Washingtonian ideal of there being no parties (especially after the collapse of the Federalists). Only because he was reticent about assimilating the old Federalists into the Jeffersonian Republicans that it failed and would later cause the 1820s splintering between Jackson and JQ Adams.
Within the United States, the only state I can think of is Nebraska, and while those elections are officially "non-partisan", we UNOFFICIALLY know the party affiliation of all the members of the state house.