I have a 2001 Coupe. Can I keep my stock Bose Head Unit and still replace all of the stock Bose speakers? If so, how does one do it?

Yep a direct swap... On a C5 with Bose the 3.5 tweeters in the front door and the 5.25 or 6.5 (depending on model) speakers in the rear can be swapped out with standard auto speakers. Most use infinity or alpines. Infinitys tend to have a nicer sounding tweeter. This alone will improve the stock system a nice amount.

Infinity's are good to go, also MB Quarts have a clean and crisp sound.

We went with Boston Accoustics, these were a direct swap from factory speakers. This was on a C6, however did have a C5 and had no problem swapping out speakers as well.