It is indeed possible, but as Aschleman said, rather compicated and usually not worth the trouble. Why not just use a really hot passive pickup? or replace both pickups? I hear the Seymour Duncan Livewire active pickup set is pretty good...although I'm a passive pickup man myself...look into it, it can be done, even email the companies whose pickups you intend to purchase and ack them for wiring advice and such, I've found they're usually very happy to help.
Lastly, I would say, dont try and wire it yourself, this will be a rather tricky pickup circuit and will probably even take a good tech a while to perfect.