How does one go about wiring component speakers (03 WRX)?

Can you take the existing speaker cables to the main unit, and wire them to the crossover? Or do you really need to put in new speaker cables back to the head unit (I'm sure that would be preferable, but I'm not sure I want to do that much dismantling of trim!)

Any help appreciated.

I extended the standard cable (use spade connectors onto the standard connector)

The run new wires from the crossover.

OK, thanks. Follow-up question: how are the existing tweeters wired?

I'm guessing that the main unit and tweeters are just wired in parallel - no crossover, just two speakers one of which isn't very good at high frequencies and one which isn't very good at low frequencies.

Is that correct? So why do you need a crossover at all? Maybe it's so that you get a sharp cut-off of frequencies to each speaker, without overlap that might interfere?