Alternatively, although it might arguably contravene the "don't split the playerbase" rule, another potential collaborative product could be a Paizo-sanctioned sourcebook describing Obsidian's Pillars of Eternity world setting in Pathfinder terms. In an interview during the Pillars kickstarter, one of the Obsidian developers mentioned how much they'd like to see such a product.
I just wanted to say how much I appreciate the graphic design of these Adventure Path volumes. As befits the subject matter, the borders on the inside covers evoke perfectly the design and feel of Russian skazki, with a little bit of a grim Golarion edge. This sort of attention to visual detail and the mythic roots of imaginative gaming are what make Pathfinder the most appealing product in contemporary pen and paper games. Nicely done!