Not quite BYO but it has a similar effect.
I used to use Reyniers wine bar in Victoria. The deal was that one paid a fixed fee for a buffet of soup, charcuterie, cheese, pud, coffee etc and then went to their adjoining (connected) wine shop to select a bottle or two. I think they may have added a small corkage. We used it sometimes for company hospitality, inviting each guest to choose a wine that was different to what we had already had and up to a maximum price.
Sadly, Reyniers shut up shop some years ago but their City branch was taken over and kept running on the same lines. I don’t know if it still exists.
We encountered the same idea this January in Parma, Italy at La Barrique Enoteca. Sit at tables in the wine shop, enjoy pasta, charcuterie etc from a menu and select one’s wine from an excellent selection on the shelves.