When playing the Black pieces, I usually like to force my opponent into the tactical battle of my choice as soon as possible. So after 1.e4 e5 2.Nf3, I mostly choose to play the Latvian Gambit (2. ..f5) (See for example this blog) or the Elephant Gambit (2. ..d5) and take him out of his comfort zone as early as move 2. If your opponent likes the Italian Game however, there’s a beautiful variation available on the Two Knights Defense, called the Traxler Counterattack. It’s characterised by the moves 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 Bc5
The strategic plan of this opening is that you ignore the attack on your f7-pawn (although that might cost you a rook), sac a bishop on f2, expose the White King, force him into the open and start your mating attack. You better keep the tempo in your game though, as you might not have enough pieces left to play an endgame! Here my try-out game with this opening against a lower rated opponent.
Conclusion: Downside of this opening is that you might not get many opportunities to play it. Even against regular “Italian” players you’ll face 4.d3 more often than 4.Ng4. But once you get your 5. ..Bxf2 in there, the excitement makes up for the waiting. Chaos, panic, (your!) pieces flying off the board at lightspeed, and the White King chased all over the board. What more could you want from a gambit?!