Ugh the Schallop defense. I've never seen Ne4 actually, always Nh5.
My instinct would be to play 5. d4 and then if 5. ... d5 6. Bxf4 c5 7. Bd3, which is about equal, black gets queenside counterplay, white a nice center and play on the kingside against the enemy king. Maybe not better than 5. d3 but there are different avenues to explore there.
Anyway, 5. d3 Ng5 6. Bxf4 Ne6 {Actually, I have 6. ... Ne6 as book, but not 6. ... Nxf3+, I think Ne6 is black's best try, but Nxf3+ is maybe just as good.} 7. Be3 d5!? {7. ... d6 is book, in Alekhine defense style} 8. d4 Be7 {c5 rightaway is better because Be7 allows 9. c4} 9. Bd3 c5 10. c3 Nc6 {Looks like a bunch of other openings right now, the French, the Alapin Sicilian..} 11. 0-0 Qb6 12. Qc2 {Qd2 was preferable I think, because of the immenent capture and knightfork} cxd4 13. cxd4 Nb4 14. Qd2 Nxd3 15. Qxd3 Bd7 16. Nc3 Bc6 17. a3
White gets a slight plus in the final position. You might miss the bishop, but black would gladly get rid of that tall pawn on c6, like in the Chekhover Sicilian, it's not really helping matters. It's a game, white can expand a bit on the queenside, but black can hold though he ought to watch out for white pieces going through the center.
And if that's not enough, you could just play 4. Nc3, interesting things happening there too.