Hello Laura, and welcome.
You can fit any sound system with an adaptor for the fascia, because the hole the stereo fits in is standard-sized.
However, because you have Blue&Me, I'd suggest doing a speaker upgrade first, and adding a subwoofer under the driver's seat, which is what I'm doing.
I've decided to keep the standard headunit as I feel the weakest part of the standard system is not the headunit but the paper cone speakers. They are a very light construction and therefore produce a lot of sound for the money (would have cost only a few quid each) including quite a lot of mid-bass, but higher frequencies are indistinct, so generally it's a 'muddy' sound. You have the tweeters (in the windscreen pillars) but again, I don't think they are the best available.
The fact that FIAT offered an upgraded sound system (Interscope) as an option which included different speakers, an amplifier, and a subwoofer under the seat, but the standard headunit, suggests to me that there's room for improvement without changing the headunit.
The doors will benefit from sound deadening, as there is not much fitted as standard. Any speaker sounds better if it is installed in a box, such as a door that is properly sealed and deadened.
Perhaps talk to your local car stereo shops - try to find one that is interested in doing a proper installation rather than merely selling you the speakers - and see what they suggest?
-Alex