I did a lot of research on this recently to figure out how to do exactly what your're asking. I wanted to keep the factory unit since everything runs through it but i wanted to power the mids and highs separate from the subs.
Do some research on the PAC Amp Pro and the wiring harness for it. There are a lot of YouTube videos on these too. It basically plugs inline and gives you low level inputs you can run to an external amplifier (or multiple amplifiers if you want to power the front doors, dash, rear doors, and subs separately like i wanted to do). Long story short it can be done and it can be done without having to cut any wires but its not cheap. At this point i've not spend any money on it yet, just been going through the process of figuring out what i want and how i'd lay it all out.
If you do go the speaker replacement route pay attention to the impedance (ohms) level of the speakers like was stated above. Going from a 2ohm to a 4ohm double the impedance and thus doubles the power requirement for the same decibel level. So you can end up with a nice new set of speakers and not get that volume you're looking for.
That's where the external amplifiers come into play.