x2... Amping the 650 helps tremendously but their bass presentation to me is always colored with its own resonant "signature". It goes beyond boost, output and freq response, its more in the realm of harmonic content, as well as transient response artifacts imposed over the fundamental tones.
I once heard DIY M^3 build that was voiced for the HD650... to excite those upper midrange tones. I think my Millet hybrid was voiced by its builder with the HD580 in mind. Amps like these are downright shouty/screechy with my K701/Grados... and unfavorably triggers the K701 weird upper midrange plastic-ey / synthetic resonance. So in a nut-shell amping to color does work... IMHO. It goes against what many consider to be the "correct" function/role of the amplification stage.
My time with the HD650 has been easier than I would have thought to amp-up. It is a fairly sensitive/efficient headphone. So as long as the amp circuit has the AC voltage swing to create a clean/undistorted magnetic field in the coil... you're good to go. Where generally more than sufficient voltage (headroom) is ideal. Not sure the exact specifics on my cmoy, but its using an OPA2107 at 2x9V... its a surprisingly effective little circuit for the HD650. Where the HD650 high-ish sensitivity really plays a factor. For reasons I can't explain, I often times like the sound of this cmoy over my 24V-PPA... which has discrete current buffer, and a 3 channel (left/right/ground) OPA627 configuration. So its MUCH "more amp", but sometimes I find it less enjoyable of a listen.