How to normalize additional skin weights?

I’m again ambitiously trying to write my own skinning algorithm from scratch in Maya, but I’m stuck at the weights normalization part. I want to insert an extra weight that works on an already weighted influence, but whose local rotation I’ve cut in half. The weight is basically the influences parent weight (A) times the influence weight (B), which isolates the extra weight to only work for points near the influence (AB). That way I can add user-specified nonlinear scaling around an influences half-plane-of-rotation similar to Anzonvin’s “ART” “mesh-spread” attribute. The problem is getting that added weight to work with the existing weights (A+B+AB==1?). Every linear operation I’ve tried to normalize the weights have failed. Can anybody help me with this?