i like 4.Nc3 fe4 Nxe4 Nf6 as black
The only one time I got this on the board with white this also my opponent played.
Atfter 1.e4 e5 2.Nf3 Nc6 3.Bb5 f5 4.Nc3 fxe4 4.Nxe4 Nf6 I never saw this before, that selden they play the Schliemann. Atter 6.Qe2 d5 7.Nxf6 gxf6 I played the funny 8.Nd4 and won the game later. At home I saw 8.d4 was the theorie. But I knew nothing!
Quite unfortunately the direct 9.Nxa7+! has practically archived the whole line as problematic for Black.
That's certainly more testing than 10 Nxa7+, but it's not so clear either. There's a very important game with 9 Nxa7+ Bd7 10 Bxd7+ Nxd7 11 f4 Qf5! - Nekhaev-Nisipeanu, correspondence 2012. And I'm currently 4½/5 as Black in this line
That game featured a clever recipe by Livi (13.a4 Bb4!?), but this is not enough. Instead of Nekhaev's 14.c3?! and the great piece sac 14...Nc5! white could (and should) trade Queens with 14.Qc4! Qc5 (forced) 15.Qxc5 Nxc5 16.Ke2, or 16.Nc3, when it is very hard to show compensation for a two-pawn deficit.