As Blumlein88, Dennis, is suggesting, you are after the sensation of the music "washing over you", in the same way as happens when listening to live musicians - it's a powerful sensation, with no downsides. Unfortunately, most hifi setups are insufficiently competent to achieve this - if you turn up the volume to deliver the necessary SPLs then all the shortcomings of the playback are far too obvious; you're unable to relax into the impact of the music, there is too much tensing of the body trying to cope with the "onslaught".
I've arrived via a completely different path from all the others speaking here, having experimented over the years to determine what matters. Surprising, and disturbing, for nearly everyone in the audio game, speakers are the least of your problems; yes, the DAC, pre-amp and amplifier are key, but what to buy off the shelf to achieve this quality is not easy to answer - my approach was to improve the working of very standard, good value for money components to achieve the necessary competence. To put it bluntly, the industry "doesn't get it", so it's not an easy solution to put together.
One approach which will get nearly everything right is, high sensitivity speakers with a good quality integrated. The right Klipsch speakers combined with a more powerful Denon integrated will deliver the "big" sound, excellent bang for the buck - there may be some audible annoyances but you should get the "swimming" from this.