I think you'd have to spend a fair amount of money until you get a worthwhile improvement over the Essence. I've been comparing my Essence ST to the Schiit Modi/Magni Uber dac/amp and the more I listen, the less obvious the differences become. The Magni sounds a little brighter but a little harsher at the same time, where as the Essence sounds warmer but more composed on the upper mids and treble. All in all the difference is very small and I actually prefer the Essence for long periods of use, as it's so relaxed sounding, but not sloppy either. The Essence runs the 650 perfectly fine in my opinion, and I've never felt like it was underpowered. I have mine on the middle gain setting (+12db) and I rarely go above 36% volume in windows. Main issue with using the Essence, is that it is in my main gaming rig, which is packed with fans and quite noisy.
Having said that, I am massively impressed by the Schiits. They are built like tanks and for something right at the bottom of their range, they look, feel and sound very premium. The headphone output is also ridiculously quiet and free from any distortion when moving the volume knob. My Sennheiser IE8 earbuds normally pick up even the smallest amount noise from headphone outputs, but on the Magni it is dead silent. The only issue I have is that there is some channel imbalance at very low volumes, not a massive issue as too quiet at this volume anyway.
Going to look at the Schiit Valhalla 2 as my next amp.