I randomly thought of this question last night:
When a Serie A team is playing a team in the Champions League from say, La Liga, do you want the Serie A team to win to strengthen the name brand of our football? On the other side, do you root against the Serie A teams due to rivalries or dislike for the other clubs? Or maybe you just don't care.
An example is, when Fiorentina was playing Bayern in the 1st round of the Champions League knockout stage, did you want them to do well for Serie A as a whole? Or did you want them to lose because you can't stand Riccardo Montolivo? I chose this example because Fiorentina isn't a hated team like Roma or Milan amongst us.