A catback system or simple replacing of the mufflers is exactly what you're looking for if you want to retain cats but add volume.
The typical Mustang sound includes going with Flowmaster, but there are many other options. Magnaflow makes a great system with either mufflers or 'Magnapacks', which are basically little bullet mufflers that allow much more sound through. SLP makes the Powerflo and Loudmouth I and II systems, but Powerflo is likely going to be too quiet for you. A lot of guys don't like the Loudmouth systems because they seem to simply add loudness and volume (not in a good way), but don't seem to have much good "tone" to them. Additionally, if you ever add an aftermarket midpipe, the Loudmouth systems traditionally become TOO loud for most to take for too long. Mac also makes a decent-sounding catback, but I can't say much for their quality as I've not experienced it. In my own personal opinion, Magnaflow is tops in terms of quality: stainless steel, great fitment and near show-quality finish, amazing durability (their mufflers won't gradually blow out the insides or deteriorate like some will), and excellent sound.
Good luck with your choice.