I had this very thing happen in my last match. The Americans were about to launch a Torch-style invasion in '42 but capitalized on an undefended Genoa (oops!), cut off Rome from reinforcement, and knocked Italy out of the war with the DAK sitting at the gates of Cairo. Then BAM, Yugoslavia and Greece were 'liberated'. With the Italian garrisons gone the allies quickly occupied the ports that were vacated and in a couple of turns cut off the DAK entirely.
The outcome of that match made for interesting possible alt-history. No American troops ever went to England, they all went straight to the Med. No cross-channel invasion occurred, and Paris didn't fall until early '45. When Germany surrendered, the W. Allies had liberated Bavaria, Austria, Hungary, Yugoslavia Greece and Bulgaria, Italy and France. Downside for the West was the Russians ended the game on the banks of the Rhine.
I love possible/probable alternate histories. Stalingrad was dumb, Kursk was too late etc etc