Question about premium sound system Options

[Coligion]

My car has the 8-speaker premium setup with two amps. I’ve replaced the two subs/drivers in the front doors with some Sony speakers (they were rattling the door panels), but I would like to know if It would be possible to power a small subwoofer in the trunk with the existing amps?

[quick_5hifter]

I wouldn't do that, I wouldn't use the stock amp with any other speakers, midrange or subwoofer.
The stock amp provides "weak" power because the vibrations can cause damage to doors and the rest of the car. That's why all the standard, factory sound systems never provide more than - let's say - 2x20w rms, 4x20 w rms etc.
You thought that, for example, Toyota couldn't create powerful sound systems like Pioneer, JBL etc., and sell them as an extra option to the car? I think they could do that, but they thought about rattle noises that might be caused by that. Not to mention that you must be able (while listening to music loudly) to hear the police, ambulance an firemen' s sirens in traffic.

I recommend you to use a 4x75 - 4x100 w rms amplifier instead of the standard one. Replace the factory 20 cm (8 inch) speakers with 20 cm kickwoofers (available from few brands - Ground Zero Audio for example). They are a little expensive, but they worth the money. In parallel, on the same channels as the 8 inch woofers, you can (and should) mount 1 set of tweeters.
In the back panels you cand easily install 6,5 inch (165 mm) kickwoofers or even full range speakers.
All of the speakers should have around 70-120 w rms, except for the tweeters (~25w rms should be enough and safe to use with amp, if provided with high pass filters).
You can also apply noise sealant (I don't know how it's called exactly, but I'm talking about Dynamat, Standartplast, Stinger, Brax etc.) inside the doors and the back panels, to eliminate the undesired vibrations and get the best out of your sound system.

I don't recommend installing a subwoofer in the trunk, just because of the weight. Any subwoofer, no matter how small it is, will weight more than 20 kilos (up to 100 kilos or even more) and I think nobody wants to add extra weight to the car. It doesn't matter if your engine is 7afe or 3sgte, you will definitely feel every extra 10 kilos.

Good luck!