You could also just yank everything stock from it and rerun new wiring, which is what I've done in my 88. From the tweeters I ran wiring to the head unit, from the door and rear deck speakers I ran wiring to my amp in the trunk. Currently, there is one amp for four of the six internal speakers, and one for the subs. For the power connection I ran direct fused connection for everything, the stock wiring kept blowing fuses. You may want to consider doing that since in my car, dunno if it was a random mistake or what, but the radio was wired in with the internal lighting on a
5 amp fuse. Basically anytime the volume went up, it blew a fuse and all the lights went out, and I'm not talking about really loud either. That was with a JVC 20w x 20w tape deck, much less the 50w x 4 JVC I have now. Got sick of that crap and direct fuse connected it, problem solved. As far as that other amp goes, its probably a bad idea to run your head unit into that. Connecting more than one amplifier to a speaker is a bad idea, as it can very easily damage one or both amplifiers, unless you have Dual Voice Coil speakers for your car, then you could run one amp on one coil and a second on the other, but you cannot run them piggy-backed like (I think) you are talking about doing. If that's not what you're thinking then feel free to ignore that comment
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It really isn't all that hard to do complete wiring revision like that, but it involves a little effort. At any rate, if you think you're interested in going that route let me know. I stripped my car down to bare metal, deep cleaned and scrubbed everything, put aftermarket sound deadener on the whole thing, ran all my wiring, then put it back together, total time on that was probably around 30-40 hours of work. If you were to just run new wiring, that would probably take 3-5 hours depending on how familiar you are with the interior of your car.