Well...this could have a few options. Alot of fatory speakers run at different ohm ratings than aftermarket. For example, If the factory speakers work at 6.5 or 8 ohm, and you put in an INEXPENSIVE speaker that runs at 4 ohms..it will pull more power from the head unit. This should only be used if it is a moderate-low price speaker replacement. THIS WILL STRESS YOUR HEADUNIT If you go to a moderate-expensice set of speakers, it might actually get quieter as the factory stereo might not push the speakers even close to recommended specs.
Another thought is replacing the head unit, which will almost always up power. You will definately increase power and sound quality, but the speakers will be worked a little harder and will fail sooner. In some cases, I've seen aftermarket headunits blow the factory speakers as soon as they were installed. Personally I would recommend saving up and doing a head unit/speakers install all at once. It will make a HUGE difference in sound quality. If you want to expange to amps or subs later, you have flexiblity if not...enjoy your new sound! It is all about what you want to do in the long run and exactly how much of an improvement over stock you really want.
John

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"I STILL LOVE BEER!"
-GOX III