Is fine volume adjustment possible in macOS?

⌥+⇧+F11 and ⌥+⇧+F12 were restored in 10.7.4.

You can do precise volume adjustment with AppleScript, controlled on a scale of 0 thru 100.

set volume output volume 0 --mute
set volume output volume 100 --100%
set volume output volume 27 --27%

You can get the current volume (also 0 thru 100):

set currentVolume to output volume of (get volume settings)

So, you can write a little script to increment the volume by 2% (approximately what one quarter square used to be):

set currentVolume to output volume of (get volume settings)
set volume output volume (currentVolume + 2)

You can make one for decrementing by changing that plus sign to a minus sign:

set currentVolume to output volume of (get volume settings)
set volume output volume (currentVolume - 2)

If you want to get the volume sound like usual, add the following line:

do shell script "afplay /System/Library/LoginPlugins/BezelServices.loginPlugin/Contents/Resources/volume.aiff"

You can save this as a script or app, and bind it to a mouse or keyboard button (if your driver lets you), give it a keyboard shortcut (as a Service or with another app), or put it in your menu bar (with an app like FastScripts).