Personally I don't think you should be able to. No one is pushing the drinks down your throat.
If the bartender thinks you're too drunk and out of compassion, or because you're pi$$ing him off, CHOOSES not to serve you, he should be able to do that, too. It's his property!
Actually, the LAW is that if the bartender gives someone obviously drunk ANOTHER DRINK, and that drunk kills someone in an accident, the Bartender can lose their license and be held accountable for the death.
I.E. The bartender has a legal right, and duty to REFUSE SERVICE.
A gunshop owner can REFUSE to sell you a gun, by LAW.
Ergo we already have precedents in place supporting any kind of business owner’s right to REFUSE SERVICE.