Which SS amp can deliver "tubish" sound character today ?
FET-output stage amps have a bit of a rolled-off treble, due to the design.
Also, any OPAMP-based amp can have the OPAMPs changed to either: OPA627s, which are a bit "warm"-sounding, or an Audio-gd Moon HDAM which has a bit of a v-shaped frequency response, intended to imitate how some tubes sound.
I would say Zana Deux or waiting for the Super 7 amplifier
Sorry, I agree with Uncle Erik is that if you want that you should get a tube amplifier
which should be according to your need. Both amplifiers that I mentioned are tube amplifiers from Craig Uthus of
Eddiecurrent.com. Zana Deux is one of the legendary tube headphone amplifier although it is not
cheap but worth every penny and very robust and reliable. If you have limited budget you may wait for his new
amplifier called Super 7 amplifier. The prototype was presented in Venice meeting 2-3 months ago
and should cost around 1499$. It will use 7 6SN7's tube and was mentioned to be a perfect match
with the Sennheiser HD8000 and LCD2. It is also a tube lover's dream because you can do a lot of
tube rolling to get the sound that you want and the tubes doesn't have to be high priced to do that.
Here is the link of the super 7 amplifier prototype which should be announced soon.
and here is the info provided by Purrin about the tube rolling which would not cost much as expected
I also cannot think any solid state amplifier that sounds like a very good tube amplifier, the closest that
I can remember is the one that I used the balanced beta 22 which is a solid state amplifier and I used a
preamplifier function of the Balancing Act which also used tubes.