Prussia, Russia and Britain are the obvious candidates (though all three in the same team is obviously very unlikely).
Italy alone, of course, does not stand a chance against France and Austria combined, and indeed would probably lose a war against either of the two (though, with France, the defensive terrain favors Italy greatly; but the power disparity weighs heavily on France's side). Italy however offers a second front, which is always useful. A vengeful Prussia might see the value of that (as they did historically in 1866). So would a anti-Austrian Russia who is not in good terms with France. Italy is very dependent on Britain (particularly for coal) so it would not join any anti-British alliance unless her rulers are in a suicidal mood (which is possible; happened IOTL in 1940 after all). For all her problems, Italy was not an insignificant player in the Great Powers equilibrium, though it is true that it was the lesser among them (or the strongest among second-tier powers if you prefer).
No other power, of course, would go to war to give Rome to Italy. But most would welcome Italian willingness to do so in case of war with a mutual enemy.