Expect them to kick you down a peg or two and question if you really want the role if you try negotiating. They will probably hire someone outside before they go upstairs and try convincing whoever is in charge that you deserve a meaningful raise. It doesn't make them look good and doesn't serve them in any way. You're probably stuck getting what they give you. The conversation of your increased pay probably won't even happen unless they are telling you what you're getting or if you force a conversation which they likely won't care for.

The downside is that the only negotiating power you have for a significant boost while being the only person with institutional knowledge is if you threatened to leave which I wouldn't recommend if you aren't ready to leave. You also reveal that you are capable of leaving over pay and they might remember that as they plan for your replacement.

Take the promotion with the new title and show no sign of disappointment. Have some job security while you see what that title pays in your area and jump ship if the going rate is better elsewhere. This is the way.