I don't think there is a way to lower the lowest volume permanently, but there is a way to make it temporarily, as long as you don't press the volume button after using this command.
Just enter this into terminal:
sudo osascript -e "set Volume 3.5"
and it will set it to 50% volume, using 0 for no volume, 7 for max. 1/4 is around 0.57, so
sudo osascript -e "set Volume 0.57"
will set it to that 1/4 increment. If you want lower, you can use:
sudo osascript -e "set Volume 0.2"
etc, etc. Adjust to whatever fits.