The best results I've seen are analogous to a modern version of rotoscoping. It involves creating a fully animated 3d model of a person and then using a well trained deep fake of the actor's face in combination.

Youtuber Shamook did just that with the finale of the Mandalorian season 2. https://www.youtube.com/watch?v=wrHXA2cSpNU

He actually got a job with ILM out of it. The future of CGI actors will probably involve a fusion of techniques like this in order to get it right.