It's not impossible.
Here's how I did SRV-sounds years ago:
SRV used muli-amp setups for performance and recording. No matter what he used, he sounded like him, but I duplicated some of that sound with the following setup.
I had a blackface Princeton Reverb and a tweed Princeton. I used an A/B/Y pedal to split the guitar signal to the 2 amps. I set the Princeton Reverb for a fairly clean sound at lowish volume, and probably set the Treble and Bass a little higher than I'd typically do when using it by itself; Reverb around 4 or so to add some depth. The tweed Princeton was near-cranked and used for a midrangey distorted sound to fill the mid-scoop space in the Princeton Reverb.
Overall, there was clean and distorted at the same time, mid-scoop and mid-boost at the same time, dry and reverb at the same time. Does Pride & Joy/Texas Flood pretty well. Yes, it's not the wall of doom he used in recording.
Output tube distortion is, in my opinion, important in this setup. But let's say you can get close-enough distorted sound from preamp tubes. Then you just need multiple preamp channels with different voicing/tone circuits, same phase relationship and able to be mixed to give your clean and distortion ahead of the output stage. It's very important that there's some consideration given to getting your distortion sound at the same relative volume at your clean sound, to get good control of the relative level of each without being limited to a single volume level.
You might need one master volume for the whole amp which acts the way Hiwatt intended their Master to work, meaning it sets the overall amp volume and was not intended to facilitate preamp distortion. I say that cause you'll need channel master volumes to force each channel to distort or not as desired.
You could go as crazy with the number, configuration, tone circuit, tube type, etc of channels as you'd like.