Remember that AST started as the Chemist job, so the card system, and Mudras are the basis for how a Mix feature would probably work; the same with Dances now.

But a few things to note:
First, I don't suggest going beyond the game in it's current form. And by that I mean, if you are making a healer, they will share healer gear and use the healer role actions. It just makes the most sense.
Second, I'm not sure if you knew this, but Chemist, or Salve-maker as it will most likely be called, usually has a high magic stat, if WHM is A than CHM is B. While the idea of them not using magic makes some sense, based on their concept, most games give them access to basic "magic" which is offset by their personal buff. Basically, they can use MP for spells is what I am getting at.
And finally, I would suggest looking up some of the ability names used by Chemist, and all related jobs, in the past, so as to get a feel for their skill set. You, and most people I feel, seem to stick to their "item usage" nature, and forget that they have a background in magic as well. So it's not wrong for them to use magic, in fact, that could be how they "mix" the items together.