4 ohm 12XN version? (or switchable impedance 12XN?)
"Can I have a 4 ohm 12XN550 to make my Super Mini, Super Compact or Big Baby 3 a 4 ohm cab?"
Short answer: No.
Long answer: The Barefaced 12XN550 driver is a very unusual animal - it can move air like a PA subwoofer yet its efficiency and operating bandwidth are closer to that of a guitar speaker and despite that its frequency response and accuracy is more like that of a high-end hi-fi speaker.
To achieve these goals required extreme optimisation of every detail of the speaker and the goals were achieved with a voice coil that gives the speaker an 8 ohm nominal impedance. Until you try to design a loudspeaker it's easy to assume that a voice coil is "just a voice coil" but it really isn't - just as a guitar pickup isn't "just a guitar pickup". The wire material, wire gauge, winding pattern and geometry all affect the tone and performance - as do the pole pieces' material and geometry and the magnets likewise.
There are two ways we can make a 4 ohm version of the 12XN driver - one way involves losing low frequency power handling (air moving ability) and thus low frequency output (which is one thing that makes Barefaced cabs awesome). The other way involves losing sensitivity (efficiency), treble response and dispersion. There is no way to make a 4 ohm 12XN that sounds the same and has equally amazing output and performance as our 8 ohm 12XN.
When people ask us about making a 4 ohm 12XN they're always doing so because they think they're never going to need a second 12XN cab and they want to get maximum power from their amp - both of these theoretical 4 ohm 12XN versions we could make would be quieter than the 8 ohm version, due to either a loss of power handling or efficiency. In reality with an 8 ohm 12XN you have a very efficient speaker which will do more with the watts you have and handle all the watts you have, so very few 4 ohm cabs as small will match it for output.
Long answer summarised - no, it's impossible to make a 4 ohm 12XN as good as an 8 ohm 12XN, but thankfully you don't need a 4 ohm one!
One more question - "can I have a 4/8 ohm switchable Barefaced 12XN cab?"
Answer - absolutely not. Switching between 4 and 8 ohm impedance on a single driver requires having either two voice coils (one 4 and one 8) or an 8 ohm voice coil that can be split in half to make a 4 ohm coil. Either approach will lead to a reduction in performance in one or both modes - so lower output and/or power handling and inconsistent tone/bandwidth between the different impedances. It's a marketing win but an engineering and thus music and gigging fail.