On the stock system, I think the inputs which send the bass signal to the rear to be amplified are line level, a function of the Becker stereo. If you have subwoofer outs on your new Alpine, you may be able to connect these to the inputs on the active base amp, with a splice job, which will power the bass woofers in the doors. However, not sure if the ohms are the same. With a new, more powerful stereo why not just add better speakers?

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2002 Mercedes-Benz E320 4Matic
1995 Mercedes-Benz E320 Wagon
2005 Land Rover LR3 V8 SE
1999 Audi A8 4.2L quattro