Does that mean we go for a third vote in the unlikely event remain comes out on top?

After all, whatever arguments justify a second vote apply equally to a third

I don't think that follows, though no doubt whoever lost would continue to campaign for one. The 2016 vote was whether to leave or not. The proposed vote is on the shape of leaving, with the ability for people to say nothing being offered is good enough.   If they decide it is not good enough, we should not do it, but certainly you are free to argue that better is possible, and once you have come up with something to argue for a vote on it.