I understand what your trying to do. You want to add and amp for the mids in the door and tweeters while using the factory amp to power the dash speakers. You can do this but its pointless. All you will be doing is sending unwanted low freq's to the door speakers.Your tweeters are the only thing that you will notice.

The problem with dsp is......

1. All the crossover functions are inside the amp, meaning if you use high level outputs the new amp is going to be restricted to the crossover freq's of the dsp amp.

2. If you want fullrange to your aftermarket amp you NEED to remove the dsp amp completely.

I went through the same thing as you. It will not work.

The only really options you have are to keep the factory amp, use highlevels for the front(6channels) and/or rear(4channels) and sub(2channels)
Or you can remove the dsp amp and get a good electronic 3way crossover and 6 channels of amp for the fronts.Something suitable would be a 4channel amp for the door/dash speakers and a smaller 2 channel for the tweeters.
You can use you other amp for the sub/s.

Now if you do this you will have no rear speakers. If you want them you will need another amp.
The dsp system is a pain in the ass to upgrade. Pain in the ass means expensive.
Most people will swap speakers and/or add an aftermarket amp and sub.(Amp for sub only)

Again I know what you're trying to do and its just not possible.