Hard to know what you mean by 'no soul' I suspect that is different for many individuals, by no soul, does that suggest a since of 2 dimensions, or lack of med-range impact, or less encompassing mid to lower base?
Best to start with your weak points in the system, I found in my system, the weak points were initially in my cables, power, interconnects and speakers cables, over time I replaced all of them.
As you mentioned, its a rabbit hole for sure, once I found that solved one problem, I went to better speakers, then a better pre-amp, and finally a better dac (only due to my theta dac had failed)
One of the biggest differences, and most expensive equipment changes were the cables, at least they dont really wear out, once you make the investment, unlike other electronic equipment
I went to NBS black label from transparent cables, ultimately that gave me the start to holography and separation I was looking for, after witch I added a better speaker, German Physiks system from Thiel CS5's, followed by better preamp and amp, from krell integrated to Einstein tube pre-amp and Halcro mono amps
Every step made a difference, because I was replacing a weak point with something better, in other words, the rabbit hole
Finally replaced my burned out theta dac with a Weiss 501 DAC, the Weiss may be a bit better that the theta, newer tech, I have a soft spot for theta, it ultimately about synergy, however it all started with the cable system, once that was set I could hear the differences in further additions, good or not so good, and make a informed decision on upgrading older equipment