OK, thinking about this question, I realised I don't understand details myself:

So, suppose we have a WAV file with a loudest possible sample, 2^15. I understand that with volume 0dB and EQ flat, DSP will send exactly that, 2^15, to DAC. Am I right? Now, with volume set to some other value (let's suppose EQ is left flat, for simplicity), DSP will multiply sample with appropriate factor (factor of 2 for 10dB or something like that, right?) What I don't know is whether DAC has input range larger than 2^15, that is, is there a danger of 'digital clipping' if we go into overdrive? 'Analog' clipping in preamp is another question.