first of all, it shouldn't be the mouthpiece, but the player. If you have lots of stamina with a 3C, which i do too, start out on that. Thats a relatively big mouthpiece, so it's going to decrease your range a little before you get used to it. Before you start working your range on it, play it for at least one hour a day for 1-2 weeks. During that period, try to restrain from going above a high C above the staff. From there, start doing the Caruso stuff. Start with caruso 1, and work your way up. If you don't know what caruso is, i'd reccommend getting the book. #1 is breath attacked first notes and play three of the same notes as halfs, start from G and chromatic up to C, making sure to breath attack each new interval. Then number two, this is a premier range builder, but you'll have to get the book.
Another thing that'll help you is slow blast top notes. This is where you start from low G, then go chromatic up to the next note, blast it, then come back down to G, and whisper the note. Continue going up the chromatic scale with this, and do it about an hour everyday along with Caruso. Make sure to do the slow blast top note at least twice as long as the Caruso, since Caruso is tiring and will wear you out.
CAUTION: If you start getting light headed, stop, rest, then come back. If your chops are blown beyond all extent, do not attempt any of the exercizes! Finally, DO NOT, I REPEAT, DO NOT try to scream into the upper register just to see how high you can go, the process will be for longed.

One last thing, only start using different mouthpieces once you've developed your range to your liking. Smaller and cheater mouthpieces are only to be used to increase your range for the period you use it, not to build up range. Never build range on anything smaller than a 10 1/2C, examples: Schilkes(tho i love them), Monnettes, Bach cheaters, Jet tones, LOUDs, and XStream. Only buy thoughs when you are done building your register.