I actually had the same thing. I retained my factory head unit but added some subs and replaced all of the stock speakers. The RCA’s are generally just providing your amp the input of an audio signal for the amplifier to strengthen and push through the subs. I have my signal tied into the wires of one of my rear deck speakers to get the signal and then all I had to worry about was making sure I get power and turn-on from the battery and head unit. If you want a good easy fix I would go the t connector route like These. Just put one on the positive and negative of your door or deck speaker and make sure you connect them correctly to your amp and you should get your signal. This is obviously for smaller projects like a daily driver or just improving your system which sounds exactly like what you’re looking for. This method will keep the door speaker powered and it will allow you to keep your factory amp without having to worry about the number of rcas on the head unit.