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.