Would also like to see Mourinho have a bigger role in the game.

I know that I'm an Admin and all but I'd like to share my own suggestion as well.

How about he becomes something like a daily (Weekly? Monthly? idk), challenge that clubs can try and tackle in order to receive a nice prize.

Whenever the "event" resets your assistant manager could write you a notice like: "Boss, Mourinho has been training his lads really hard this season. Our sponsors are offering quite a reward if we take a victory from him. So? How about it Boss?"

And several ways to gauge your overall preparation for a meeting with Mourinho's top players:
a) We're really out of shape. Lets gather the lads and start some more rigorous activities to compensate on the resent down time.
b) We're looking good. Some more training would go a long way to cement our chances though. Let's get on the pitch show our determination!
c) Squad's in great shape, Boss. There's no moment better than now to take on Mourinho's boys and show 'em what we're made of!

Damn, this feels more like we're talking about thugs and mobsters going after the kingpin. haha
Well you get what I mean, I'm sure.

His squad can cahnge up in formation and mentality, strategy, etc. Each time, or perhaps a rotation of popular formations, that you have to beat?
Yeah actually why not the latter?
He can offer formations that you have to beat, this way you can test your thinking and learn how to counter your opponent.

I personally really like games where I'm offered a PvE challenge that resets at a certain period of time or when specific conditions have been met.

/Pokes Voldara - My feedback is ready for you to report to the devs, Voldy! :P

Joking aside, Mourihnho's club can be turned in to a fun feature of it's own, a game inside the game, if you wish.