It is tricky for sure. And I’m not any good at it myself. As my mixes are pretty flat and weak. But a few things come to mind.
When everything is loud, nothing is loud. So have quieter elements in your mix. Experiment with compressing those quieter layers. Not too much, just enough.
And have dynamics in your arrangement. But too much dynamic range and it doesn’t compete anymore in the commercial space.
I don’t know about you. But when it comes “mastering” my track I often tend to throw a compressor/limiter on it. Maybe some subtle EQ moves and “done”. But the better, professional mastering engineers do a lot of additional things to get it all sounding good. For example pushing up the volume on the quieter sections so they hit the compressor too. And post compressor automate it down in volume again to retain “the drop”. But quieter part does get some of the same compressors flavor and feel.
(high quality) Outboard gear does seem to add something to the three dimensionallity of a sound. I don’t have any fancy gear myself. And no, I don’t think it is a magic bullet. Still, sound as current moving through opamps, transistors and tubes changes the sound. I’m not saying you can’t achieve fantastic results in the box. Cause people certainly can. But getting some harmonic distortion from the real world does seem to help / make it easier. Basically get (some of) your digital sounds out of the computer at least once. Be it during recording, mixing and/or mastering.
Getting your reverb pre-delay and decay time to match the speed and style of your track is another important thing.
Arrangement is super important. More important than my earlier points. What is playing at the same time? And what is it playing. Is it another layer of the same sound playing the same pitches. Or is it an independent musical layer. Generally, the less is playing simultaneously, the more room there is for it to sound better. But counter melodies can add musical depth to your tune. So make space for it.
None of these by themselves will make it magically 3d. But a couple of subtle moves combined can have a large impact.
Hope it is of some use to you.