What you describe, as I understand it, is the exact problem in ``Overdrive''. The problem is that there is no value past the maximum value, and if you try to amplify that digitally, then you get some clipping.

Here's an example (Note that I've decided that the range of samples can run from 0-99, which easy to look at, and that each click on the volume knob increases sample amplitude by 1. Both of these are not accurate, but not too far off reality for demonstration purposes.):

Let's say you had a series of samples in a song that looked like this:

34 48 84 94 98 99 97 89 70 53

If your volume control is set at 0, then this is the exact set of samples that reach the DAC. If you increase the volume by 5, then you'd like to get the samples:

39 53 89 99 103 104 102 94 75 58

but the maximum sample amplitude (again, for the purposes for this explanation) is 99. So the samples that would actually get sent are:

39 53 89 99 99 99 99 94 75 58

So you lose data. Assuming that your system is set up to not blow speakers at normal levels, it's unlikely that going into this digital overdrive would blow them. It just won't sound as good. Then again, if you get severe clipping, it is possible to damage your speakers due to the odd signals that will end up getting sent to them. It seems to me that it would make more sense to increase the output of your amp slightly to make it so that you don't have to get into overdrive. But then again, someone with more analog electronics experience than me should probably correct these last few statements.