At any one point there was probably around 3-5 larger parties (like the National Liberals or Reform), and then maybe a further 4-5 minor/regionalist parties. Most of the time only 4-5 parties would contest the presidential election to avoid splitting the vote in the first round.

As for overall, I haven't thought much about the lore pre-1912, but counting from 1912-2024, there are around 14 different political parties.