Thinking about distorting signals led me to think of effects pedals, whiles thinking about merging signals led me to think of my Roland TR-707 for its individual outputs.
The result here runs the drum outputs through various pedals, then merges them together again.
I've used a Bass Synthesiser pedal on the low tom and the Talking Machine pedal on the high tom, as well as Space Echo on the high hats and a Lofi Machine on the snare.