Maybe there isn't a limit of three random events?

[TomD]

I'm not sure removing the cap is a good idea. Reading through dozens of "witch's curses" every turn doesn't sound like fun to me.

Hmmm. I wonder if you could try using a turmoil-3 misfortune-3 dominion if you had enough forune-tellers/seers to remove the bad events in your own provinces and push it on to your neighbours? It would also make someone think twice about invading if they knew they were going to get hit by barbarian invasions in every province they took every turn.