Which SS amps sound like a tube amp?

None. There is no such thing IMO.

mcintosh, classe, odyssey

Your Parasound amp has the power and control you need, so what about simply buying a decent tube preamp. It'll probably do what you want and cost less than a good 200 Wpc tube amp...

and if you want, they also have a tubed pre...

I agree with Ncarv about the Levinson No. 27. (Although that has only 100W/ch).
The No. 23, which I upgraded to from the No. 27, does have 200W/ch. I paid $2000 for my used No. 23 about 5 months ago. (If you can afford it, I suggest buying the No. 23.5, although it usually goes for around $2,500).
It has a "touch" of that tube sound that sounds so good. I used to have a CJ MV 50 many years ago, before I upgraded to the Levinson No. 27, so I do know what the tube sound is all about. The bass in these Levinson units is very tight and deep.
You will not be disappointed in these units.

Good Luck!