Sub Install question (kinda long...)

[Tombodad]

First off, I know theres an article and I read it (very informative, btw) but this is more theory than practical stuff.

So, I am under the assumption that adding an aftermarket sub to a stock system, when properly done, benefits the system in two ways: One, it provides more bass, and Two, because of the more bass, the stock speaker's bass can be turned down, allowing them to produce better sound on mids and highs. Is this true?

Again, assuming the above is true, on a system with a stock sub, such as DSP, if you were to simply tap into the stock sub's signal to run the new sub, would you then be able to turn the Bass to the stock system down? Wouldn't this affect the signal into your new sub? And, even if you could turn the stock bass down at the headunit, then just pump up the bass at the amp for your new sub, would that affect the sound quality vs having the stronger signal in the first place?

Forgive my ignorance, and the long post, but I am new to the whole ICE thing. Much more of a mechanical person...