Some time back I had a silly idea of a Germany vs. Italy war, called the "Ace and the Deuce" where instead of Hitler, the Red Baron survives WWI and becomes Kanzler of Germany.
Then Mussolini's ambitions lead France and the UK to support a German effort to annex Austria and then club some sense into Italy.
It might be possible, in the case of a German-Italian War over Austria or something for Germany to try to create a puppet government in Northern Italy. But this would be a nasty affair and my suspicions are that the Italians would hate this situation and get violent about it.