is there any way to hook up after market radio double din pioneer 5500 to factory amp with the bose system on a 03 996

 

The Bose amplifier you are referring to (code named Autobahn) has a MOST input; it can not directly interface with an analog/line level output head unit.

Since there isn't really anything special about the Bose amplifier outputs, you could just remove the amp and install a new one to connect to the stock speakers.

It's been done many times for 996 cars on RL.