The mechanics required to shift flexible facial appliances from a neutral expression to one other convincing expression should be relatively straightforward, once a designer establishes what the start and finish expressions should look like, and the fabricator comes up with the the appliances' shapes and their material makeup. Something 'in between' may even be possible, with the proper linkage location. If you want to add a third distinct expression, now one has to consider adding another set of 'facial muscles'. If you're lucky with that, you may gain a fourth usable expression. Lots of math, and or trial and error involved. Guided cables, and the occasional bell crank would be good choices of primary mechanical components.
This is all theoretical, based on seeing and/or building similar working mechanisms. I have never worked on a fursuit.
I spent over a year prototyping a fursuit head for a friend. It involved a fiberglass 'skull-muzzle' and a ton of music wire, brass tubing, a jillion Dremel tool cutting disks, 2 part silicone rubber and too much lost sleep. We also used 4-way stretch fleece, the high end stuff, different types of foam and NFT 4-way stretch fur. BTW, the design was also a Use Your Own Eyes head.
The basic issues are whether you want radio control of expressions (not recommended unless you want a giant head for servo room) or expressions using your cheek muscles, forehead movements and chin extension. My method REQUIRES the skull-muzzle fit you exactly, no slop or movement whatsoever. That means you need a lifecast to work off of. Also, it takes about fifteen minutes to get the head on correctly, since there is some prosthetic glue involved so the head is on for the duration. We always used a hair dryer with the cool-low-high switch epoxied in the cool position for cooling off in the headless lounge.