Mouthpieces are not meant to be interchangeable, as they change the embouchure of the player (which will only impede the musician's ability to play). It can take months to years of playing to fully transition from one mouthpiece to another, and changing them around in the middle of a show would not have a desirable effect.
If you want a different sound, there is a wide range of ornaments that can be used (flutter tonguing, triple tonguing, scoops). However, they seem to be less common as corps desire a specific sound from every player - and they are resorting to synthesizers for musical effect.