As far as I know, the only way you can change ability sets when playing online is to die at the hands of another player or get stunned in a "team" game. Unfortunately it's just not possible to commit suicide without getting assistance from your pursuer and it's inconvenient giving free points to a pursuer/target just because you want to change abilities.

Are there any other methods to be able to switch ability sets in the game that I'm not aware of?

_{On a side note, this question stems from this PC bug that prevents me from changing ability sets in team games between rounds. I don't get the "round changing" screen, I'm just left wandering the map until everyone else spawns which makes playing team games for me very frustrating.}