The Stomvi multiple cup system discussed in 2 posts above is called a combi system. It offers a series of cup depths for the trumpet shank bottom ranging from A to F cups. The kit can be set up with flugelhorn or cornet shank bottom as the second bottom choice. The combi kit is not widely popular in the US market and is not listed on the Stomvi USA website. The Stomvi Flex mouthpieces are far more popular amongst US players.
Estuche Combi System Trompeta / Ref. 8000 | Stomvi
The combi kit is an interesting solution to finding different cups that provide the tonal qualities a player is trying to achieve. The combi system was not developed for commercial players it was developed as a solution for the player playing different trumpets Bb, C, D/Eb/ F, and Pic.
The OP was being specific as to the one type of mouthpiece their teacher is interested in having them use.
“My professor at my university wants me to play on a different mouthpiece for playing lead jazz and solos in marching band”.
This points to a commercial mouthpiece as it applies to this individual. Based on the rest of the OP’s comments the recommendations offered guides the OP towards mouthpieces in their rim diameter that are medium depth as apposed to shallow. This is a logical place for them to start.