6.0-0, favoured by George Koltanowski, transposes to the related gambit line 4.0-0 Nf6 5.d4 following 6...Nf6, when 7.f4 and 7.Bg5 are the main possibilities for White; however, 6...d6!? is an independent alternative for Black.
6.Be3, dubbed the Miami Variation by Jude Acers and George Laven, is a way for White to deviate that probably suffices for dynamic equality.
Acers, Jude; Laven, George (2003). The Italian Gambit (and) A Guiding Repertoire for White–1.e4!. Trafford Publishing. ISBN1-55369-604-2.[self-published source]