If she says she can't share, maybe she really can't. For what it is worth, every time I have tried to change someone, it blew up in my face. In hind sight, this would have happened less if I had listened to what the person was telling me instead of hoping they were mistaken.
I would be pretty uneasy if someone who told me in clear terms that they couldn't share was continuing to date someone I was with. My last relationship got cowboyed exactly like this.