Why do you need so many triggers? Sometimes its a sign of the puppet not being set up correctly. E.g. I use “a” for angry but the one key is hooked up to mouth, eye brows, eyes etc - it changes them all at once. Sometimes people think you can only bind a key to a single trigger and not share it.
MIDI is a clear answer - 88 extra keys on a midi keyboard! There are other midi devices as well.
But if there is a logical grouping to your triggers, you can nest them. E.g. have one trigger for angry under which there are say 10 hand positions. A second key for happy can then reuse the same 10 triggers for different hand positions. So yes, combining two triggers can effectively multiply the number of combinations ... if the puppet is suitably structured.