I have two idea's for events that would span over several days depending how long you wanted the event to run for.
My first idea is like OSRS's king of the skill. You had X amount of days to train stats and get the highest total level possible. Think this would be a fun idea depending on the game mode you chose. Say the event was based on knight mode maybe you have 48 hours to get as much xp possible in those 48 hours of gametime, not IRL time.
My second idea would be starting on fresh accounts and and you had lets say a week of playing and getting drops and at the end of it, the person who has the biggest bank value wins. No donating and everyone would have to be on the same style account to make everything fair.