I'll detail a few times where the sound was transcendent for me.
Back when I was in my second year of University, I had a pair of Rogers LS3/5a. Source was a VPI HW19/ET2/Grado MCX, Audible Illusions IIB preamp, Counterpoint SA12 amp. The speakers were placed at the opening to the dining room, no side walls for about 4 feet, and about 7 ft from the back wall. The speakers completely disappeared, and on some vocal recordings, it transported me to the recording venue at low to mid volumes. Not quite totally believable, but amazingly involving nonetheless.
My first encounter with the Martin Logan CLS 1. I had been searching for the fabled Infinity RS-1B that many senior writers for TAS had said were among the finest speakers. Couldn't find any local dealer who had a pair. Heard the RS-2B but didn't hear any magic (might have been any number of reasons). Discovered High End Audio by accident. Arthur, the owner, played the CLS for me. The track was Weavers at Carnegie Hall. The midrange, voices was eerie. Again, I was transported to the original event. Sure there were weaknesses, but when it was right, it was stunning. Other recordings didn't have the same magic due to the weaknesses, but on that album... Many years later, I have the CLS 2Z on custom Sound Anchor stands, and when I play them with Martin Logan Depth subs, clients tell me they are just as amazed as I was/am. With this set up, many more great recordings can cast the same magic.
I had the good fortune of helping David Wilson set up a pair of Wamms. When it was done, the result was again, magical. Even recordings that were not "great" created a life-like presence that I've not heard from many cost-no-object systems.
For me, I believe the requirements are, in no particular order:
1. The system has to disappear. Both soundstage and image must be fully detached from the speakers. Some speakers do a great job of throwing a stage between the speakers, but not when the stage gets close to the speakers.
2. Depth, presence and Height. Some systems "produce" great depth but at the expense of a laid back front stage. These systems always produce the sound behind the speakers regardless of how the recording was mic'ed. I find that this detracts from my ability to suspend disbelief. When I play Johnny Cash singing "The Beast in Me", he should sound like he is in the room. Conversely, Cowboy Junkies "Trinity Sessions" should transport me to the Church of the Holy Trinity. Height is an interesting one for me. Wilson speakers from the MAXX up create a tall image, and that seems to really help. Speakers that may be arguably "more coherent, faster, etc" but are 40-50" tall don't seem to create that illusion for me as easily.
3. Accurate fundamentals and harmonics. Too lean and the illusion is gone. Similarly, too rich and I am bothered by the tonality.
4. Dynamics - played within the capabilities of the system/room. Too loud or too soft, and the illusion is gone. And volume must also be a function of the instrument. For example, playing back a cello at too high a volume level and the illusion is gone. I leaned this from Arnie Nudell and Mark Levinson years ago. Both were careful to play at "correct" volumes.
5. PRaT.
6. Illusion of air - from the lowest frequencies to the highest, it seems to me that when the system can move air, the system disappears and I am in the venue. Note that this does not necessarily have to do with bass. But if the system doesn't go low, properly, it's hard to create the illusion.
There's probably more but I'll stop here for now.
Again, these are MY experiences, my opinions only. Just sharing to see if anyone else has ideas.