Can +bow skills stack on Zon bows?

[Zyr]

I just found a three-socket Reflex bow with +1 to Amazon bow and crossbow skills, and it got me wondering: If I were to put the Melody rune word in the bow, would I end up with +4 to bow and crossbow skills (in which case, I'd be better off hunting for a three-socket +3 Matriarchal or Grand Matron for my hypothetical Ko rune)? Or is the bonus to bow and crossbow skills capped at 3 (in which case a faster and/or higher damage bow would be a better Melody candidate)?