Triad
It has long been the custom in the Empire for large consortiums of mages working together (typically at a tower) to appoint a ruling triad of the three most powerful mages. The number three is traditional, but it is theorized to have been chosen in order to form a minimal ruling body that nonetheless can never be deadlocked. This practice has gradually declined as the Empire has tightened its control over the study of magic.
The Avernite Triad
When the Five created the Tower of Magi, they adopted this custom.
The Triad controls the Tower of Magi and therefore all magic in the Kingdom of Avernum. However, in practice, they do little of the day-to-day administration required in the Tower, and instead focus on their research and politics. There have been several combinations of archmagi in the Triad - no mage has been a member of every Triad. However, the Triad was recently disbanded, due to the Crown's request to have tighter control over the Tower.