Tron uses zero buttons on the plate, DOT uses 1, and Xenophobe uses two. I've never seen one with more than two on it, and it would be a pretty tight fit inside- those volcano buttons are bigger in back than they are out front. You might be able to get more buttons if you used a different switch- but I don't know what games you would want them for. Maybe PC games?
If you wanted to go crazy, you could mount a POV hat from a PC stick on there, that would give you 4 inputs on the thumbplate.