Will Step Up Transformer Improve the Sound Quality?


I'm wondering whether a step-up transformer would improve my analog signal path.  I have a VPI Prime Signature with a Dynavector 17D3 Karat cart.  My phono stage is a Parasound JC3+.  The rest of the path is a PS Audio BHK Signature Preamp and a Pass Labs X-150.8 amp into Spatial Audio M3 Turbo S speakers and dual REL S/3 SHO subwoofers using Audience cables.  I am looking for advice as to whether adding a SUT would markedly improve the sound.  I am also looking for recommendations as to which SUT's would work well in this system.
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Again, thank you.  I appreciate the expertise here.  rauliruegas , I agree that the JC3+ is a fine phono stage.  As for the REL's they are utilized for the lows below 32hz which is the bottom end for the Spatial Audio M3 Turbo S.  It provides a great bass foundation.  You can really hear the difference when they are off.  The bass is tight and fast with no bloat.  
and if you heard my rig your jaw would drop.


So would you take the Pepsi challenge...?!
Like everything else, it depends.

First thing is how your phono stage is made. Some have lots of gain built in, and are nevertheless quiet - when I DIYed my phono/pre, I built in lots of gain, and spent time and money to make it quiet. Dead quiet. I also built in a very fine SUT, the top silver Lundahl, because I have a Miyajima mono cartridge, and it hums unless isolated by a transformer.

I marginally prefer the electronic amplification to the Lundahl SUT (which, by the way, is the best I've ever heard, including a 10K unit) because it's just a touch clearer and just a touch more dynamic. But that's with dual unobtanium input devices in parallel to reduce noise. Otherwise I would definitely prefer the Lundahl. YMMV
To build in SUT inside isn't the good one idea. It will catch more noise so SN ratio will be inferior compared with external one. Friend of mine builds tube phono stages so customers usually wants SUT inside as it makes less space and less wiring for it. Although the same external SUT performs better.
Mostly for SUT he uses Lundahl various types. And they are really good ones but nothing spectacular. But from the price point Lundahl is the best, IMO. If to hear spectacular you have to look for artisan designs some of them are really good ones. Then you'll find your favorite you'll forget active gain stages, head amps etc.
More noise? Less noise if you shield carefully and keep AC far away. Or so it seems to me.

Of course if you put an SUT near a high voltage power supply you are asking for trouble.