Here's a schematic and selection for the wires.
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Any green wire from the selections in this harness is going to be the negative. I also did not hook up the subwoofer lines. From the factory, the wires from the harness are going to go directly to the speakers of the Bose system. Knowing this, I took the leads from the harness and fed them into the inputs of my DSP/Amp, and then connected the outputs of the DSP/Amp to the remaining leads to the Bose speakers.
Below are schematics that have been shared in this forum that helped out immensely! Thanks to all the members who have shared the wiring diagrams within the threads!
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What was really nice about this project thus far was that I planned this build over a year ago. I felt maybe it was completely out of my league, as playing with factory installed amplifiers get scary. Musicar Northwest is a professional installer and in no way can I say that I am an industry professional. However, their venture yielded fruit that inspired this project! With confidence, I can say that as long as your "premium" speakers are 2 ohms or above, procuring a DSP/Amplifier that is stable at 2 ohms will suffice. As crazy as this sounds, you might be able to utilize just a multi-channel amplifier (rated 50 watts @ 4ohms) to increase the output/clarity for the Bose system instead of overhauling all the speakers for better performance. These days, there are plenty of multi-channel amps with hi-level input that are affordable.
I won't lie though, this project took a span of three days, granted the drama, meeting my brother's boyfriend's family, and a Sunday BBQ.