Ever seen a 3 villain superhero movie being correctly handled?
Superman II
4 villains: General Zod, Ursa, Non, and Lex Luthor
Batman Begins
4 villains: Ra's Al Ghul, Carmine Falcone, Scarecrow, Victor Zsasz
The Dark Knight
4 villains: Joker, Two-Face, Salvatore Maroni, Scarecrow
The Dark Knight Rises
6 villains: Bane, Talia al Ghul, Ra's Al Ghul, Catwoman, John Dagget, Scarecrow
X-Men
5 villains: Magneto, Toad, Mystique, Sabretooth, Senator Kelly
X2: X-Men United
5 villains: Colonel William Stryker, Lady Deathstrike, Magneto, Mastermind, Mystique
X-Men: First Class
6 villains: Sebastian Shaw, Emma Frost, Azazel, Riptide, Angel Salvador, Magneto
To name a few.
And you can't come back with "this guy was in the movie too little," etc. Your question was how many films had 3 villains in a superhero movie and handled them and the story correctly.
The priority is the hero's journey. In all of these films, the story of the hero/heroes were benefitted by the addition of the villains. The fact that you wouldn't consider Scarecrow to "count" in
The Dark Knight Rises (for example), doesn't mean that he's not a super villain who was in that film -- and that on the whole -- that film worked.
Just saying that it CAN be done. It HAS been done. Hopefully, it's done well here.
But, like you, I grow wary when I see this many characters in one film.
-R