Hmmm. So many interesting comments, so little real analysis.
So, let’s do some physics and math so everyone can at least be on the same page.
Every amplifier is constrained by its power supply. No amplifier can make more voltage or provide more current than its power supply can make available.
Few amplifiers (in fact none that I know about) can swing voltage fully from rail to rail. Amps stop at some voltage less than the rails, depending on circuit and components, so that active devices don’t completely cut off.
So let’s say our stat amp PS is +/-400V rails. For the sake of discussion we’ll assume for the moment that the amp can get as close as 50V to each rail. This means that the amp is swinging +/-350V. Since it’s a differential amp the true output voltage is twice this, or 700V. And this leads to a peak to peak voltage of 1400V.
Of the schematics that I know about, including the LL, the KGSS (headwize article), BH (headwize article), and the KGSSHV (published schematics), most of these amps will get to 50V (possibly less) to the rail before the active devices may find themselves in more non-linear portions of their curves. I am not privvy to Stax schematics.
I don’t know what the BHSE’s rails are. The LL rails are 400V. If the BHSE rails are the same then they will make about the same peak to peak voltage swing. I have published 1300V for the LL to be conservative in what I am saying, but it will actually make 1400V. I don’t know about the Stax amps, but if they also have 400V rails, the outputs will be about the same.
If the amp has higher rails it can do better. For example, the KGSSHV has 450V and 500V options (based on what I know). Using the 50V approximation, this means that the KGSSHV can do 800V peak and 900V peak respectively. Which translate to 1600V and 1800V peak to peak. Perhaps a little more.
If you need this kind of voltage swing, I honestly recommend that you build or have someone build you a KGSSHV. Personally, I think it is a pretty cool amp, as I do the KGSS. I have said so publicly on several occasions. But, this doesn’t mean that they are the only options worthy of consideration as some of you clearly do.
Now, one can argue that some amps can get closer to the rails before showing higher distortion. Yes, possibly, but then we’re not talking about huge differences in peak to peak voltage swing if they can get 10 or 20V closer.
Someone mentioned RMS voltage. So let’s talk about this. Which RMS voltage are you talking about? The RMS of the peak to peak or the RMS of the peak?
For 400V rails the peak voltage is around 700V. The RMS of this is about 495V. The LL can do this, despite my conservative spec. Any of the other stat amps with 400V rails will do about the same. Those with higher rails will do more. So, if you’re going to compare, then freely compare, but compare the same thing.
Furthermore, as we know, most music will not drive any amp continously to its maximum voltage, only on the dynamic peaks. I rather suspect that you wouldn't notice the difference between an amp with 1400V peak to peak vs. one with 1450V peak to peak unless you specifically chose something to evidence this difference.