1. Neck Strap Height. Make sure your neck strap is sufficiently high. A neck strap that is adjusted too low can result in an unsupported approach to embouchure which produces a certain deadness in the sound.
2. Mouthpiece position on the neck. If your mouthpiece sits too far in on the cork (meaning pushed in to move the pitch center sharper), you can end up with an unsupported embouchure again, this time compensating for a pitch center that would be too sharp with an embouchure with sufficient pressure for a full sound. For the following to work, you have to have a good sense of pitch and intonation. To experiment with this pull out or push in your mouthpiece by just a millimeter. If you go a little too far in (on the sharp side) you'll hear a deadening of the pitch, if you are a little too far out (on the flat side) you'll feel a certain tightness of embouchure that doesn't allow for fluid inflection or full depth of tone. Dead center you will find that you have a comfortable embouchure and a fuller sound.
3. Ligature position. You can also maximize the fullness of sound by finding the optimal ligature position on your mouthpiece (meaning it's position towards the front and back of the mouthpiece). The ligature affects which parts of the reed vibrates and different ligature positions produce different timbres and response to air flow and articulation. Experiment moving you ligature to different positions to find out what you like the best. You'll find the further you put the ligature back on the reed the more core or mid range vibrations you will hear in the sound. If you go too far it can begin to sound dead as you lose highs. I've found an optimal position for me that is a good balance between highs, mids, resistance, and response to articulation. I initially wanted a few more highs in the sound but I instead opted for a stronger core which has the added advantage of being slightly more responsive to articulation.
4. Long Tones, Overtones, and Multiphonics. Finally, players who practice long tones especially overtones and multiphonics tend to have more vibrant tones. Even just a day or two of going without my regiment of overtones results in a deader tone. Daily maintenance in the area keeps my tone alive and vibrant.
Alright, good luck with everything, and please consider experimenting with my suggestions before making a decision on the horn!