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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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.
I have various SUTs, special Headamps, High Gaing MC phono stages (with adjustable gain), MC phono stage with built-in SUT is the quietest of them all ... 

What is really special is Current-Injection type of MC phono which I also have (for low impedance MC).

I like simplicity, less wires, I would like to use just one box instead of two. 
But if you like different flavors you must try what you like in your system! Don’t ask others what you will like. 
If you want to try a SUT there are so many top quality SUTs from the Japanese manufacturers, inexpensive classics from the 70’s, 80’s. 
If your cart is low impedance try Current-Injection type of the MC phono stage instead of the SUTs