For example something like the Mages Guild Council of Mages or the DB Black Hand possibly replace The Elder Council?
A lot of mages in the Mages Guild are involved in politics; how else do they secure their monopoly of magic and allow members to kill others who practice outside, even if they're completely benevolent? Hell, Ocato used to be the Archmagister of the Mages Guild, but retired because the duties of being The Imperial Battlemage and Archmagister were too taxing together.
Also, the Dark Brotherhood have assassinated emperors before, but never replacing them. They're assassins and businessmen, not politicians.