OK, so you record something in Audition and the average levels are -11dB. So far so good. What are the
peak levels?
-11dB is actually a pretty good average RMS for most material, perhaps a little loud but that depends on the type of music. If it's modern electronic dance music, that's a genre that expects very high RMS values. I'll assume that's where you're going, and that -11dB is too quiet for you.
If you're getting audible distortion after raising the volume, it's because your peaks are exceeding 0dBFS. You just can't do that without making it sound bad. In order to increase the perceived volume, you need to raise the
average while limiting the
peaks to under 0dB. For that, you need a limiter.
If you insert a limiter (such as SONAR's Concrete Limiter) into the master bus, it will prevent the peaks from exceeding acceptable levels. You can then push up the volume without uncontrolled clipping. You may still hear ugly artifacts if you push it too hard. That's because you're distorting the waveform, possibly resulting in aliasing. The trick is pushing it just hard enough to achieve your desired loudness without going too far.
There are lots of other tricks for getting a mix louder, such as bus compression and multiband compressors and selective EQ, but start with a limiter first.