If you want to stick with Audio Physic, then the old, 3 box Caldera is phenomenal. Not quite truly full range, but close, and with a Storm 3 (which is also what I have) you won't care. I heard these only once but they left a lasting auditory impression, and they were the holy grail to me for many years. They originally retailed for around 20,000 dollars and appear RARELY on the used market.
I've never heard the Avanti III's, but owners on Audiogon seem to love them, and they appear to be VERY highly regarded, which is no surprise to me.
I've never compared these head to head with the Virgos, or even heard the Virgos, but in my opinion, the Intuitive Design Summits are phenomenal. However, their rolloff is around 40 hertz, similar to that of the Virgos you already own, so they're not truly "full range." Even so, I believe that they have better bass than the Paradigm Studio 100 V 3's I owned just before them. That was a huge, huge HUGE surprise. One caveat with that is that the preamp was changed and the Dodson DAC was added, and the amps were worked over. But to give you an idea of their bass capabilities, my Rel now has its crossover set at 27 hertz, whereas it was at 28 hertz with the Paradigms. Still these may seem too similar to your current speakers (at least on paper) to be a viable option.
If you want a truly full range floorstander, consider the Intuitive Design Denalis, which are said to be flat down to 16 hertz. All you need is 65,000 dollars and you're done....except for cables and stuff.....I've never heard them but can sort of, maybe, kind of, possibly, imagine based on how phenomenal the Summits sound.