OnePlusTwo, The Beta22 is considered by many as the ultimate headphone amplifier, at least in the Solid State realm. It should be a major step up from the CK2III. Also, it can be configured as a 2 channel, 3 channel active ground or fully balanced (4 amplifiers), making it very versatile (and the fact that it AMB designed it to be built that way from the beginning.)
I don't know if anyone has done it, but an option after building a CK2III, would be to build a second one, and use them both in a Balanced configuration (Of course you would have to rewire your headphones for Balanced operation).