I dont recommend having the bose amp being a part of your music. One amp feeding another amp is not good no matter what processor you put inbetween. Some people dont mind the quality, some people do (me)...especially since (in my opinion) this bose is crap.
You can pick the signal up before the amp but you will lose voice nav/phone/auto volume/etc. and i believe total volume control. The audio goes into the amp strictly 2 channels left and right; your processor would be responsible for splitting it into 5 channels so it needs to be a good one to avoide phasing. If you go with a processor capable of splitting it into 5 channels for your front, rear, and sub, that processor most likely comes with a remote so you can control the volume from inside. You just have to decide if you're willing to lose the other stuff. I dont know how much you ACTUALLY use that stuff, but i dont think you'll miss it.
If what people say is true and only music comes directly from the headunit what you can try is take the left and right audio before the bose input, and then take the ch 1 & 2 speaker output, splice those together and feed your processor. That will give you
1/ your music untouched by the bose.
2/ your voice navigation/phone and volume control of them (not your music) from the headunit
3/ the nav/phone however would now come out all the speakers instead of just the front.
Now everything i just stated is strictly based on reading the schematics and my years of doing stuff like this. I didn't actually test this scenario out, but i havent been wrong in anything I've attempted so far

lol. So take care on how you cut wires in case it doesnt work as you...or I...expect so you can solder it back if anything. Also, I'm saying this based on 2008+.