It would be awesome to see a headline in the middle of December pop up and say "Swansea Manager Sacked!" and then have him replaced by Middlesbrough's manager or something like that. Even if there was a coaching carousel like in the NCAA Football games at the end of the season it would be great. It could also lead to more in game transfers between AI controlled teams as new managers need players that fit their style of play.
To answer the OP, it would be cool to control multiple teams such as a top Champion's League squad, as well as a League 2 team, and maybe something in another league like an MLS or South American team to keep things interesting.