Apple - Can I lower the minimum volume on my Mac?

This only gives you one more notch below 1, but it might do as much as you need it to. Use the decrease volume button to lower the volume to 0. Then, press the Mute button once. This will let sound play, but at a lower volume than 1.

Also, you can change the volume in 1/4 increments with the following shortcuts:

• ⇧ + ⌃ + volume buttons in Snow Leopard
• ⇧ + option + volume buttons in Lion or later

An alternate way to control the volume is one from the terminal. For example:

sudo osascript -e "set Volume 3.5"

This will set the volume to 50% (the scale is 0-7 using the terminal).

You can use whole numbers or decimal numbers. A higher or lower number will make the volume go up and down in intensity (again 0-7).

This will put your volume at super quiet:

sudo osascript -e "set Volume 0.1"

This will put the volume at an even quieter setting:

sudo osascript -e "set Volume 0.01"

As @timothymh stated, for 1/4 (0.25) increment control without the terminal, you can hold Shift + Option while using the F11 or F12 keys to adjust the volume by 1/4 (0.25) increments.

Using the keyboard will only give you 64 adjustments of volume control 16*4 = 64

Using the terminal you can achieve 700 options for volume control 7*100 = 700

starting in 10.7.4 (and versions prior to Lion) you can adjust the volume in 1/4 the normal increment. You can get down to 1/4 bar using ⌥+⇧+F11 and ⌥+⇧+F12