Edge of breakup dynamics are absolutely possible with many solid state amps. If they weren’t, I wouldn’t use them.
The reason is because circuit designers have spent the last 40 or so years getting solid state amps to respond and sound like tube amps. Try comparing a tube and solid state amp from the 70's or 80's and you'll probably have a different opinion.
Every time these threads come up I get to see how many people obviously haven’t played a solid state amp in 30-50 years, yet are totally convinced they know what they sound like and what they will and won’t do.
It’s always fun.
My JC77 is 40-50 years old. My whole playing style relies on true dynamics (not the fake, squashed, cooking tube kind). But real dynamics: clean-to-distorted AND quiet to loud. The JCs smaller than the 120 do it all. For me, the dynamics chain is guitar volume/right hand, amp, and one OD. Our songs range from clean to distorted. I only use the OD for lead/lift. All other dynamics and shades of dirt come from my hands, guitar volume and the amp. I also use delay and chorus. I'm not some sort of purist.
I think there is a lot of truth to the post that said you can either dial gear in or you can't. And if you can most gear works honestly. A quality SS amp with a quality MV works better for me than tube because I don't want squash. I want dynamics. Good SS gets in the way less for me and is less "goldilocks" to sizing the amp to the venue.