Tubes produce even-ordered harmonic distortion, often in easily noticeable amounts, like 1%.
Bipolar transistors produce odd-ordered harmonic distortion, but usually in smaller amounts, like 0.1%.
FETs, V-FETs, HexFETS, and MOSFETs all produce even-ordered harmonic distortion, but usually in smaller amounts, so they don't sound quite as tubey as tubes, but are objectively more accurate.
Output transformers seem to make ss amps sound more tubelike, even though they don't change the distortion from odd to even harmonics.
So... if you want tubelike sound in an ss amp, look for an amp that uses one of the FET varieties. Some of the smaller Hafler MOSFET units come to mind and of course the Sony VFETs (rare and not cheap). Beyond that, ss McIntosh amps that use autoformers will get you part-way there.
Some ss amps are "voiced" to sound tube-like, but, as the Carver demonstration showed, that voicing is inherently unstable, meaning that if you change speakers, it might be gone, or still there, or different. Pot luck.
Or... you could use any good ss amp and a tube preamp, or... a ss preamp and amp and a tube buffer. Our sponsor Grant Fidelity makes two of those, I think:
Tube Processors. Musical Fidelity used to make a reeaally good one, but it's not at all cheap, then or now:
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