Amplifying pre-existing fault lines to encourage general weakness is certainly one that's been well explored. Another might be amplifying political or ideological that serve the foreign power's goals (e.g. general pacifism when that power is planning some kind of aggression or military build up, or electioneering messages for a candidate with a more favorable trade policy to that power).
No one could deliver particular results with certainty using any of these methods, but they could definitely put their finger on the scales.