Lost in Transfer

A short question. Is there a way to keep any blend shapes on an armature if you append a model from a different file?

I assume you mean shape keys on a mesh, that are controlled by an armature? No, shape keys are part of the mesh, not the armature. But if you append a new model, the shape keys should come in with it, if you created them. Then it’s a matter of setting up the drivers again to make it work…