What generally happened with the Democrats is that the party machine in the state decided if they favored Douglas or Breckenridge and the Democrats in the state went along with that. The Democrats were divided on the West Coast, so both Douglas and Breckenridge were competitive in California and Oregon. In Pennsylvania, New Jersey, New York and Rhode Island ran "fusion" slates of electors who would vote for Douglas or Breckenridge depending on how things looked when the electors voted. New Jersey voted for a mix of Republican and Democrat electors so Lincoln and Douglas both got electoral votes from the state. Lincoln carried the other three states, but there was a split between the Fusion ticket and Douglas loyalists in Pennsylvania, so it looks like a lot of people favored Breckenridge when they were voting for the Democrat party line, rather than a small group of rebellious Douglas loyalists.
This is already getting interesting and we only have nominees from the third party.