This is one of those impossible questions that forces us to identify our priorities and our biases. First, I'm assuming that by 'soul' the OP means an intangible quality that conveys the music to the listener in a way that is more compelling, more alive, more lifelike, than simply reproducing the program without noticeable distortions or unnatural artifacts. Beyond that- and I'm not even sure that's a 'neutral' definition, we'd have to start with the owner/listener's taste, preconceptions and preferences. A hard rock listener is going to look for things that somebody who focuses on chamber music or small jazz combos might not and vice-versa. (Granted, the theoretical ideal that a high resolution, full bandwidth system capable of great dynamics, resolution and all of the other attributes should be agnostic to the type of music is just that, an 'ideal'- systems involve compromises, even at stratospheric prices, and for most people, the compromises are drawn sooner). So, I'd want to know what the user/owner likes to listen to, and at what volume levels. Next, the room, how big, its acoustic properties, and how moving air in the system at different frequencies and by what means (planar, dynamic, omni, horn) is going to trigger sonic anomalies and whether the owner/user listens near field, is willing to be confined to a sweet spot, or wants a more consistent sound field throughout the room. What kind of acoustic treatment will be necessary, depending on the type of speaker and its placement in the room? Are there compromises in set up due to living conditions, or is it a dedicated room? Has the AC been sorted? All of these are threshold issues.
The equipment: sources- vinyl only, multiple sources, or digital as main source? This may affect how the rest of the system as well as the room is 'tuned'.
Equipment synergies- obviously, just buying the 'best' (whatever that is at any price point) and combining all those 'bests' in a system is not a system. No news there. This is probably where a lot of audiophiles get stuck- and it results in constant equipment changes. See synergies, below. Kinda hard to predict in isolation.
Isolation, physical and electrical. From equipment generated resonance, to vibration and footfalls, to electrical/electro magnetic, to extraneous noise (and I'll lump in here electrical isolation from appliances and grounding issues among equipment)
Sensible allocation of resources among the components, including cables. It makes no sense to have a killer turntable and crapola to play it through, or conversely, a fabulous speaker system and insufficient amplifier power or quality to meet needs.
Likewise, there are those more subtle interactions between components that define synergy. In my experience it is pretty hard to predict how a given component sounds in isolation from the system it has to work within. So, borrowing, getting a loaner, etc. to try it out in the system makes good sense- the alternative is to keep buying and replacing equipment to get it right.
Set up- all those tweaks matter. In addition to isolation- cable dressing, attention to best practices in what outputs, impedance, loading, bi-wiring configurations, etc.- may require experimentation. I'll put to one side tube rolling, which is its own sport.
Warm up, break in, etc.
A willingness to experiment with placement of equipment after the system is initially set up.
Keeping everything up to snuff, retuning, bias, cleaning contacts, checking things occasionally, all makes a difference.
Where does this leave us? Perhaps with a well-chosen, well set-up, well thought out, well maintained system that meets our expectations for making music. Will it have soul? I have no idea! Much
depends on what your personal definition of 'soul' is- I could happily listen to a pair of old Quads with a small tube rig and a turntable and find more soul in that than a monster, full bandwidth state of the art assembly of the latest and greatest that has not been put together as a system, recognizing all of the above. So, I still haven't even come close to answering the question. But it certainly is worth thinking about why some systems give us some quality that goes beyond 'loud' or 'deep' or 'clear' or 'big' and reaches something in us that makes us connect better to the music.