Can interconnect cables improve sound stage height, width, and depth?

Absolutely not! Wire is just that - wire! IC's are simply signal conduits - they either work or don't work! They are not tone controls or equalizers! Save your money for something that really matters - like speakers!

You’ll hear more musical info in the areas where you previously couldn’t.
It will be more detailed, have better focus, and be more in balance with what you already hear, giving the impression that it grew.

Just having less toe in with your speakers  will increase the soundstage more than better interconnects. But by all means, use better interconnects.

As for your last question, I use Darwin ICs and they helped "grow" my soundstage. 😄

All the best,
Nonoise

I'm a skeptic when it comes to fancy cables.  Any well-constructed cable that meets the specifications of whichever standards apply to it should be audibly indistinguishable from another such cable.  

You may see differences in oscilloscope readings for various cables, but the big question is if any of those differences are audible.  

To my knowledge there hasn't been a rigorous double-blind test published that shows a statistically relevant audible difference between any properly constructed cable vs others, if there is I'd like to read it though.  

Out of boredom, I swapped out my Darwin ICs for an old pair of Mapleshade copper ribbon ICs and then, a pair of Zu Audio Mission ICs to see what would happen. 

With both of the older copper ICs, I was rewarded with a pleasant, slightly fuller/denser presentation. Highs were recessed compared to the Darwins and it had that nice, reproduced sound to it.

When I put the Darwins back in, the sound became more focused and had that "I'm now in the studio" presentation. The shimmery highs returned, the bass tightened up, and it became much more realistic, in every aspect you can think of. There was no comparison.

Use your ears.

All the best,
Nonoise

Some years back, I had decided to replace my Silver Audio Hyacinths, and gotten a pair of Wireworld’s Platinum Eclipse interconnects. With the Hyacinths, I was enjoying a wall to wall sound stage(with attendant, accurate, imaging) and excellent/realistic height and depth(with recordings made in open venues, that contained the ambient info). Installing the Eclipses, while realizing more air, greater inner detail and tone quality, the sound stage was reduced to between the outer edges of my Magnepans. I then auditioned a pair of Synergistic’s Tesla Apex, which yielded EXACTLY the same benefits/audible improvements, as the Eclipses, but- restored my sound stage width. They’re still in my system. Besides using my own recordings for sound stage verification, I like the tests(especially the LEDR) on the Chesky CD: http://mazsola.iit.uni-miskolc.hu/~drdani/cdlist/chesky.test1.html and https://www.audiocheck.net/audiotests_ledr.php Prior to that experience, I had replaced a pair of Audioquest Emeralds with the Hyacinths, which was tantamount to removing a blanket from over the speakers. YEAH- interconnects make a difference!   https://www.stereophile.com/features/772/index.html