The bad news is - If only.... it is not as simple as popping to the local hi-fi shop - in fact, only one or two people on this forum have attempted it with any success. If you remove the factory head unit - the car won't start!!! So it has to be stashed in the dash or vehicle somewhere.
However - the good news (for you) is that you've come to the right place.
If you look in here http://www.saabcentral.com/forums/showthread.php?t=12703
at the Stereo category you will find some of the many stereo upgrade threads that have been discussed in previous years.
In brief, the Saab 9-3SS uses a fibre optic digital audio network which makes it easy for Saab to add and subtract options. However it makes it very difficult to upgrade to anything that sounds decent because there are no "good" signlas to amplify from the source components (radio, CD). The solutions to date have been to use the speaker level outputs as inputs to additional amplifiers.
Replacing the standard speakers is a great first step and will make the stereo sound significantly better than standard.
Depending on your standard stereo set up (4, 7 or 13 speaker) will then determine how you proceed from there.
So the answer to your original question is - yes it can be done, but you really really have to want to do it because it is very involved. If you just want better sound quality and a bit of bass, or aux-in capability, then all this is relatively straight forward with the factory stereo. Have a read around and do a few searches and then decide what you want to do.
A lot will depend on what you want - bass / audiophile stereo / something listenable; and also how much you want to spend - £100 or £2000. There is something for everyone possible.
Do you have 4, 7 or 13 speakers? My advice for each system would be:
4 speaker - buy the Saab 7 speaker upgrade (about £250 plus set up by Saab) and then replace front and rear speakers (not doors). Possibly add an amp to get some bass from a pair of additional 6x9.
7 speaker - replace all the front and rear speakers (not doors). Possibly add an amp for more bass with additional 6x9s.
13 speaker system - change the speakers and then see what you think.
Hope this helps. Feel free to ask questions - but check out the other threads first to avoid repeating the same topics. This is discussed on a weekly basis.