It is using the outputs, this will introduce a few things to the system that will have to be accounted for.
1) is delay, without anything extra you cant accomidate the time delay becuase of the extra amp
2) you will introduce noise, in the aspect that you are running amp-converter-amp-crossover-speaker. Just too many things in the system that will degrade quality.
3) you will still have to deal with the crossover frequencies that the BMW amp is output. You can trim them but not excede them.
Again my opinon, bad idea. Just better speakers will help some, with clarity and if you get a higher sensatitivy speaker with volume. But overall you need an overhaul.