Have a look at the Schliemann (3 ... f5) Or the Bird Invitation (3 ... Nd4)
Against e4 with black

First of all, I am assuming you meant 3.Bc4. If you did, then the Schliemann and Bird are out (rooperi probably interpreted your Bc5 as Bb5, but based on your Hungarian comment I am pretty sure it's Bc4).
There is a tricky sideline in the Two Knight Defense. It is probably bad, but I bet you will catch many players with it. It goes: 3...Nf6 4.Ng5 Nxe4. This line fits your request above. Of course, White can go for 4.d3 and spoil your fun, but that is true in almost any line with black, so there's not much you can do about it.

Why would you need to switch from the Two Knights once you were >1600?
In my oppinion it's not such a sound opening when you're over 1600-1700. At that point you might want something bolder such a Sicilian, Alekhine, French, Scandinavian...
Greetings.

Even though I play the Sicilian, I don't agree riuryK, since the Ruy Lopez is sound at GM level. So the question is what do you play after 3.Bc4? The way I see it, there are two main options, the Two Knights and 3...Bc5. Seems like most high level players prefer Bc5.

The other choice in the open game would be the Petroff, which sometime in the future (if I find the ambition to learn another opening) I might try.

The main reason I, don't play the Petroff is that I have spent a lot of time and effort learning to play the Black side of the Spanish. The Two Knights is handy to know if White doesn't play the Spanish. I think playing 3...Bc5 requires knowing a lot more theory, and allows White to play his pet line. I especially don't care to play the Black side of the Evans Gambit.
First, thanks for the help guys,
Im not an active chess.com user as i have ICC so im not sure what my rating would be, but I did mean hungarian(Be7) although it looks passive, Na5 to take the bishop on e4 and f5 after castle both are pretty fun to play, i'll look into your suggestions and i was also wondering what your thoughts are on the Caro-Kann and im not sure what this is called, but e4 e6 d4 d5 (also if it helps im quite sure the opponent im preparing for plays exd5)

You can play the Caro-Kann until you are a world champion. Even then you don't have to stop.
The main lines are easy enough to learn if you play otb. It's contains basic lines that can be easily understood and memorized at any level. There are options to attack queenside or kingside depending on the variation you end up playing with.

e4 e6 d4 d5 is the french, and exd5 here is the exchange french. I usually see it from people who want to avoid theory-it's probably not the best way to play against the french, and I'd play 1...e6 more often against people who favor the exchange. The fact your opponent often plays exd5 might mean he's well versed in the ideas of that line, though.

I have recently switched the open games, namely: Two Knights Defense, Modern Defense to the King's Gambit, Berlin Defense to the Ruy Lopez, and more. The great thing about playing these is that Black almost always gets a game. I used to try the French, but I realized I am a bigger fan of space than I originally thought, and tactics are the way to win. Also, the benefits of the French defense are not really evident at my low level. I am all about the classical responsed to 1. e4. Also, in the Two Knights, after 4. Ng5 there's the Ulvestadt, which sacks a pawn in most variations but you get the bishop pair and a wicked counterattack. I always like putting white on defense, it really ruins their day.

Also, these openings I mentioned are opening you can grow into as a player, and branch of from while still maintaining the themes in your plan. I think it's a great varied way to respond to 1. e4
I like the french defense against against e4. you can really get some good counterplay queenside as black. I like 2 knights defense as well, but learn some 2 knights theory and beware of fried liver attack from the italian game!

http://www.chess.com/tournament/hungarian-defense
I recently have been playing the Hungarian Defense. I am reasonably happy with Bird's Defense against the Ruy Lopez - it is a bit kooky , but I am happy with it in general. I think I am becoming even more happy with the Hungarian Defense. I know it is a far cry from the Ulvestad in the Two Knights, but it does eliminate the pesky Fried Liver, and gives Black good chances to play for a win.
I have set up a tourney, if anyone is interested in trying it out. If you like a positional approach to defending the Italian Game with good chances for a win, you may have found your new defense!
Hi, I play hungarian defence as black against e4 (e4 e5 Nf3 Nc6 Bc5 Be7), but i want something new, i was wondering if anyone knows an opening where white really has to know his lines to not mess up or there are a lot of traps you can use as black. Or if anyone has any solid but uncommon openings that can get most e4 players out of their comfort zones please let me know. Thank you in advance.