ok, i believe Pulseaudio will drive things a little harder.
Open Pulseaudio controller, goto "Output" TAB,
You will see dB, with alsamixer set at full ( 100% ), you'll see you can increase the dB gain there, try this. see if it helps.
Update:
Yes you can temporary overdrive the output, but not set it,
I noticed it started distorting over 110%,
So it is one of those " It is what it is " moments, ( meaning it's the best you'll get via mobo chip's on any Linux distro).
If you have a spare $10 or so ( i assume their cheap these days to suit your mobo ) & purchase a sound card, if you like your music/movies/etc, Greater advantage's/etc.