According to Autocar, the answer is a riff on "Definitely. Maybe." The British magazine says that Aston Martin and Bertone want to do the deed and are investigating a "small-scale production run," but how small remains anyone's guess. Autocar hypothesizes that if fewer than 10 cars are made, they will be built in Turin near Bertone's headquarters. If the run is larger, however, production would likely be at Aston's home facilities in Gaydon. Of course, there are legal hoops to jump through, naming concerns, and all other manner of nettles to negotiate before the Jet 2+2 can transition into production reality.
So... how much for this still-theoretical, limited-edition couture-n'-kiddie-hauler? Your guess is as good as ours, but the donor Rapide starts above $200,000, and one has to assume that such limited volume would confer a much higher price on the Jet's flanks. Whether that means that it could be costlier than the nearly $300,000 Vanquish remains to be seen.