a significant premium especially if "Tiffany" is printed on the dial. It is important to distinguish between vintage and modern.
Regarding vintage, many retailers were allowed to have their name on the dial. Cartier and Tiffany dials are the most highly prized double branded dials. But we should further differentiate between time only and complicated vintage. There seems to be a much greater interest (and premium) for double branded dials in complicated watches such as perpetuals. The retailer's name in the moon phase register IMHO balances out the dial. Recent auctions include 2499 Cartier and 3448 Tiffany. If you look these up you will see a major price differential.
In modern, other than a special edition, eg Wempe anniversary annual calendar, the only name that can appear on dials is Tiffany. While some people dislike the double branding or consider it neutral at best, I think you will find with minimal research more about how Tiffany affects asking prices. I understand that 2 57111/As are coming up at auctions this Fall. It will be interesting to see what the market says through bidding.
I have purposely avoided being more specific about values to hopefully not transgress Forum guidelines, but I do think double branding is a very interesting topic. While value is always interesting, what is even more interesting is collectors' views on aesthetics, because regarding investment value, watches should be above all else an investment in one's enjoyment of a coveted watch.
Best, patekova