Easiest thing to do is to lower your gain on your current amp to level off the output. Gain is used to magnify to input signal, if your gain is set too high, you WILL overpower the rest of the system.
What you are asking to do is not easy, and will take a lot of time splicing into the stock bose amplifier to get the proper signals. Not too many people have tried it here. The proper way to do it is to replace ALL the stock speakers and bose amp. Since the stock speakers are 2ohm, it makes things a lot more difficult to just replace the stock bose amp with another one. On top of that, you have the left front door, dash x3, right door, rear doors x2, and rear pillars. Total of 9 speakers without the sub.
Best way and what I would do is:
New component speakers in doors
New speaks in rear doors.
New 4 channel amp powering them.
DO NOT use dash speakers or rear pillar.
From my BOSE WIRING GUIDE:
https://www.infinitiscene.com/search/1/?q=4773-BOSE-Wiring-Diagram
Left Dash and Left Front Door: Positive- Blue
Negative- Black/White
Center: Positive- Red/Blue
Negative- Black
Right Dash and Right Front Door: Positive- Brown
Negative- Black/Red
Left Rear Door: Positive- Light Green
Negative- Black/Yellow
Right Rear Door: Positive- Orange
Negative- Black/Pink
Left and Right Rear Pillar: Positive- Green
Negative- Green/White
