Something that I don't recall the rules ever covering is character advancement of forks, to be more specific beta and delta forks. I'm not worried about alpha forks as they are a full and complete copy of the original.
I'm inclined to believe that beta forks can improve the same way that the original can be advanced. They are copies that were put through a process that strips skills and memories. They are otherwise undamaged.
I don't think that delta forks can improve themselves. They are ALIs given a personality, memories, and skills donated from the person they are intended to resemble. Improving these would probably involve the same process as improving ALIs (which isn't covered by the rules last I checked).
Gammas are a wild card. They are a product of something gone wrong. Its fair to say that no 2 gammas are alike. No standard solution for fixing them, let alone improving them. I'm not sure what kind of rules to use to do anything for these poor souls.