You might want to read this write up on how repairable different glues are. "Reparable" in this case meaning, "How well does it stick to older gluelines, either the same glue or different glues?"
http://forum.woodenboat.com/showthread. ... Repairable[sorry about the bit rot on some f the photos in that link. It's been a few years.]
TL;DR — Nothing really sticks to cured PVA glues, except for good epoxy, including other PVA glues. TiteBond, TiteBond II, and TiteBond III are all PVA (polyvinyl acetate) glues.