I'd concur that integrating a good sub effectively with a pair of speakers definitely improves upon soundstaging abilities of the mains in my experience. These improvements have been in the 3-dimensional depth and width of soundstage, and in pinpointing and resolving images in space. It does not, in my experience, however, do anything to increase the "vertical soundstage" (from your original post)...or at least what I'm interpreting your meaning of that to be, which is to say, the scale of imaging. Though more impactful (did I just made that word up) in ways I have never found it to increase the scale of the images produced by the mains. I have certainly heard systems where the scale of the imaging seems larger than life, as it were (I'm assuming this is what you mean by "vertical soundstage"). I'm not sure that I'd appreciate that on a long term basis though. Perhaps. It certainly is a novel experience when I hear it. I wonder if the novelty would wear off. I don't know what qualities speakers/system need to have to pull that off. One such system that impressed me that way consisted of NHT 3.3's and all top-shelf Levinson gear. It wasn't my cup of tea, but it was memorable and impressive in many ways. The scale of everything it reproduced seemed larger than life, and the space it was in was quite large itself, both in footprint and volume. A piano seemed larger than it should in real life and human vocals made the singers feel like giants in some way. If you are looking for this from a speaker/system that doesn't already render something like it already, I don't think a sub will move the sense of scale in that direction. Apologies in advance if I've misinterpreted your meaning.