I don't see anything in that circuit that would absolutely not work at 24V supply. However, you might have to tweak some values in the sidechain (the part of the schematic that controls the LEDs and thus the gain/compression). A schematic is at
http://www.freestompboxes.org/download/file.php?id=14315&mode=view .
I think the 2 series diodes at bottom right are providing a 1.4 V offset voltage from Vbias (0.5 Vsupply) to limit the signal when it goes above 1.4V. If you have larger signals you might need to change those (insert more diodes?)
The 560 ohm resistor at bottom right, between the output of the last op-amp in the sidechain and the 5mm yellow LEDs, is a current limiting resistor for the LEDs that light up based on the signal voltage after it passes through the limiter. With larger signals, you may need to increase this resistor to tune the compression to work well.