Splitting up a 4 against 3 pattern into 12 equal parts doesn't really work except at a very slow tempo. You just need to get train your brain (and hands) to do different things at the same time.
A good way to learn to do this is set a metronome to a slow tempo corresponding to one "beat" per bar. Start by tapping with each hand separately for several bars. Then alternate one bar with each hand, and finally put both hands together.
Three against two or three against four is fairly simple. Here's a snippet of organ music where you have 3 against 2 both with your left hand, simultaneously with 5 in your right hand, and 4, 6, 5 and 7 with your feet, on successive beats.
Trying to count out "7 against 5 against 3" by splitting up to beat into 105 tiny parts isn't a practical idea!
Drummers ought to be able to keep four different rhythms going at the same time - one with each hand and one with each foot.