I agree with Conzipe, switching openings may not be necessary but I don't think it's really harmful, and surely tends to make the things more interesting.
Against e4 with black

I generally stick with my Black Repertoire, but I do change up my white openings. Although even with White, I tend to play different variations of the same openings.

Two Knights for the open games? Interesting.
C55: Italian Game - Two Knights Defense - 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6.
In the open games after 1.e4 e5 for the under 1600 crowd, me, would you recommend 3....a6, the most popular continuation in the Ruy Lopez or 3...Nc6, the Ruy Lopez: Berlin Defense?
After 1.e4 e5, Black may not want to play both Nc6 and Nf6 right away, perhaps too passive, if White plays 1.e4 e5 2.Nf3 Nc6 3.d4, the Scotch Game, as an example.
In the Scotch Game, I prefer White's chances if Black adopts a kinda two knights defense after 1.e4 e5 2.Nf3 Nc6 3.d4 Nf6 4.Nc3 exd4 5.Nxd4.
Much less common for Black would be The King's Gambit after 1.e4 e5 2.f4, but knowing a few short responses doesn't hurt.

Against the Scotch 1.e4 e5 2.Nf3 Nc6 3.d4 cd4 4.Nxd4 Nf6 is the main line. Black certainly has to be well prepared for the King's Gambit if he plays the open game.

Please endulge me while I say that as an u1400 player it's rewarding for me to be able to follow the references to openings using names or moves or both - finally. It's almost beginning to sound familiar. Of course I have no idea what the continuations are or even why choose one over the other, but I am finally almost able to follow the discussion. This is like learning a new language. Thanks to all for the contributions.

I definitely do NOT recommend the Berlin Defense for the U2000 crowd. Kramnik was able to make it work because he doesn't mind scrounging for a draw as Black. It's an incredibly difficult game to defend, and does not give Black many counter-attacking chances until he's survived 10-20 moves. It's for exactly this reason that I don't recommend 1...c6 either.
I know there are many coaches who think the Closed Spanish is too complex for U2000 players, but I don't see anything wrong with teaching the Spanish Marshall to novices. It's tactically sharp, it shows that material isn't everything, and it's fundamentally sound.
Masters can lose as white in the opening to it, and yet GMs can defend the endgame, as Akopian and Adams have repeatedly shown.
The Anti-Marshall games are interesting, and don't require huge amounts of theory to play relatively well as Black.
I don't mind studying traps in the opening as long as the opening isn't based purely on traps. The Spanish is an excellent pedagogical tool in that respect, teaching the novice the distinction between good traps and bad traps.
Thanks for the opening ideas.
GM Ronen Har-Cvi has a ten part video series on the Marshall Attack over at the Internet Chess Club. The first video is over one hour in length!
I like it. Black gambits a pawn, gaining one tempo for development.

Why don't you try the McCrackin gambit.......1.e4 d5 2.exd5 e6 3.dxe6 Bxe6 4.Nf3 a6 5.Be2 Qe7 6.d4 Nc6 7.d5 O-O-O
Neat idea, but 4...a6? That takes the steam away from Black's attack. White is back in the drivers seat. Better is 4...Nf6, developing a piece with tempo for the pawn gambit.
No games found after 4...a6 and about 20 games found after 4...Nf6 from a 5 million plus game database. All under 2200 and Black lost 15 out of 20.

Sicilian is too complicated, and the Two Knights Defense leads to boring games in my opinion.. how about the Caro-Kann? I play it and I'm a huge fan of it, out of the roughly 30 or more games I've played against e4 as black this year, I've only lost 2 using the Caro-Kann
I agree with Estragon. The Hungarian Defense is far too passive, and the Schliemann and Bird can't be played against the move order you discuss.
Play the Two Knights and stick with it until you're +1600 here.
DO NOT GO SWITCHING OPENINGS EVERY FEW MONTHS!
Though I agree with the do not switch openings every few months, there are masters (2200+) at my club where the 2 knights defence is their staple defence against Bc4. I'm sure you could play the two knights right up until at least 2500+. Was there not a game played in the 2010 US Championship in the 2 knights?

The two knights defense can be exciting for two novice chess players and a serious challenge for any GM. Tons of theory and sharp lines abound at the top level. You can't just wing it.
For a few of my elementary music students new to chess, I have them start the game after the four knights position has been reached - then the clock starts ticking. The moves that follow are of a much higher quality and they get more enjoyment out of the game. I even enjoy watching the games more.
I hate to see young kids start by pushing a pawn only one square, and it is usually a side pawn, not a center pawn.
With the four knights, a lot of quality development has taken place and diagonals are open for the bishops at f1 and f8, with castling soon to follow.

Hm okay, but they should know / be told that after 1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 the natural 4.Bc4 ?! is not really good because Nxe4 ! and the Black is gaining the upper hand already.

So what's this supposed to suggest ?
It suggests that there are good reasons b6 is not popular for Black and c5 is.

I often play the Caro-Kann almost exclusively, while I try not to be so selective and play 1...e5 or the French.
I am not sure what you mean by playing Two Knights against d4, perhaps something like Mexican Defence ? Not very popular but playable.