Can I use a SUT or head amp with my 60dB Coph Nia MC phono preamp?

Interesting, tlarwa.  Some of the First series of Pass amplifiers, good though they are, do have a relatively high input sensitivity, which is to say that most amplifiers are driven to full output by about 1V input or less, but I think some of those First Watt designs require more input voltage.  You might look up the characteristic of the J2.  This would be no problem with the typical CDP, which puts out 2V, easily.  So it could be a combination of high-ish input sensitivity of the amplifier, marginal phono stage gain, and the fact that your system lacks the typical boost in overall gain usually provided by an active linestage.

I just looked it up; the J2 requires 1.4V for full output of 20W.  This is a rather high and fits my prediction above. You don't mention what speakers you are driving, but that would enter into the equation, as well.  If you've got 100 ohm sensitive speakers then my analysis may fall apart, since you are then using around 1-2W at most.
I've always been curious about the First Watt series; I bet the J2 is a great sounding amplifier.

By the way, if your phono can make 60db of gain, that's equivalent to a 1000-fold gain in voltage.  If the cartridge is making 0.4mV at the standard stylus velocity, the output of the phono stage is 0.4V.  With many if not most amplifiers, this would be sufficient to drive the amplifier at least close to its full output, and stylus velocity gets much higher (faster = more voltage) during musical transients.  So, I think it's the combination of factors I outlined above that leads to your sense of lack of adequate gain from the phono.

Lewm, I'm driving Klipsch Cornwalls.  My listening position is about 9 feet back.  Line I said before, I can get to the low 90's, which is typically fine.  But I'd like to have more in reserve when I need it.  I'll probably just replace the Coph Nia at some point.  There are a lot more cartridge choices in the .3-.5mV range than in the 1mV range, and I don't really want to be limited by that.  If I had a phono stage that had 66dB - 70dB (or a little more) of gain I'm sure I'd be fine.  I know there are some quality dual mono designs (which the Coph Nia is) out there that get into higher gains like that.  

The alternate cure is to use an active linestage.  That typically adds 10 to 25 db of gain, and you'd be good to go.  The Cornwalls are ultra-sensitive, to be sure.

You might even talk to Nelson Pass. He may be able to suggest a way to increase the input sensitivity of the J2.  He's always tinkering with his designs.  That would be a lot cheaper than buying a new phono stage, most likely.  In the price range where the Coph Nia once lived, you might consider the iPhono2.  For $500 it may be a bargain.