I've heard different stories from many folks and some say that CA will not adhere well to cured CA and some say there's no problem at all.
I myself have had mixed results. Back when my Dad and I built flying models made of balsa and tissue... if a glue joint had to be repaired the best results were had if the old CA was removed. If it was not removed, we noticed that the joint was more prone to failure.
In the end, though, when all else fails... ask an 'expert'.
I was able to talk to a rep for a hobby adhesive company and although I don't recall all of what he said I do remember that the adhesive performance of CA for different materials and surfaces has something to do with the purity of the CA and that, in general, uncured CA does not bond all that well to cured CA.
Fade to Black...