Each character only gets 3 quickenings in the license board so in the end it will be spread out: 3 for each. In the beginning I'd get 3 characters with 3 quickenings ASAP so you can do the combos sooner.

Also, Little Blue here thaught me a killer strategy for quickenings: Leave them to the end of the fight, because after a certain level all bosses get extra strong when their HP is critical and that is when quickenings can really make a difference.