CK²III or CKKIII (when I forget that the "squared" symbol is alt+0178) stands for "Cavalli Kan Kumisa III", a do-it-yourself design that is built by, among others, MisterX (a member on the forum) and thrice, proprietor of Rockhopper Audio. You can read about it here:
The Cavalli-Kan Kumisa III Stereo Headphone Amplifier
thrice just announced a demo program, too:
http://www.head-fi.org/forums/f29/ck...1/#post3904605
As to voltages....a lot of the better amps run on what amount to 24 to 30 VDC supplies (as single supplies at +24 to 30 VDC, or dual supplies at +/- 12 or 15 VDC with respect to ground), but can run on less. Most of the DIY amps don't include the power supply on the board, allowing the end user to decide how sophisticated a supply should be used.....ranging from the commonly used 24 VDC Elpac wall-wart for $35 or so, all the way up to designs that might run $200 or even more.The CK²III has a power supply on the board, which simplifies matters somewhat!
I had a PIMETA (another great little DIY amp) for a year or so that I powered with an Elpac at home and an 8xAA adapter to provide 12V for occasional portable use; I didn't find the difference to be earth-shattering. While it certainly seems that the relatively low voltage sensitivity of the HD580/600/650 should benefit from an amp that can provide higher voltage swings, my HD600's were driven quite capably by Ray Samuels' Predator on USB power only at the recent Chicago meet.
A lot depends on the type of music and your typical listening volume, but I wouldn't rush to get an additional headamp just yet until you are satisfied that it will add something to the Duet.
If I were you, I'd get the Duet without hesitation and put my name on the list for the demo CK²III. If you don't find that it provides the improvement you seek, then you're probably looking at a much more expensive headamp in the long run!