2004 mitsubishi eclipse infinity amp

My son has a 2004 mitsubishi eclipse with the factory installed infinity radio/cd head.  We are about to embark on the install of a kenwood KAC-8152D amp with 2 polk audio db104 subs.  As he is new to car audio, and I am just old, we need a bit of help.  The question:  The infinity system has a factory amp under the passenger front seat,  I want to tap into the rear speaker outputs at the connector to the amp and run speaker wire back to  the speaker level inputs on the amp.  Will this work?  If i understand correctly you can't run an amplified signal to another amplifier, but the outputs from the factory amp to the factory speakers are just speaker level signals right?  So it is ok to tap into the factory speaker outputs from the factory amp and run them to the speaker level inputs on the new amp to drive the subs...right?  Hope this is a little clearer than mud.  Thanks for the help.

Ken