You do not need an outboard amplifier with the HD 800 headphones. If you don’t like the signature of the HD 800, you will be better served by buying a different headphone than spending more on an amplifier. The HD 800 is a storied headphone and I have bought and sold the HD 800 S and HD 800 more times than probably anyone.
I might have a slightly different view on this. I believe in fact that the HD800 is, still to this day, one of the most tonally neutral and transparent headphones around. At least among the ones I've tried (which are the vast majority of the high-end headphones of the last 6/7 years). I find that these characters, tonal neutrality and transparency, make it for a relatively easy headphone to fine-tune, should you not totally get along with the way it sounds. I'm all for analytical sound and, as such, have always enjoyed the way it is, even combined with other relatively "dry" gear (e.g. DAVE, XI Audio Formula S, etc.). But over time I've also had the chance to test it in combo to a range of other sources and found fairly easy to, for example, lose a tad of the hyper-detail in the highs, in order to make mids and low frequencies reacher and smoother. Try to combine an HD800 with a Violectric V281 for example or a Viva or, as in my main current setup, a Riviera AIC-10 (with the right triode valve - e.g. most of the Mullards).
In my experience, the only aspects of the HD800 which are difficult, virtually impossible, to correct are its total lack of any "visceral" bass reproduction, which actually affects most of the high-end headphones (with possibly the only exception being the Abyss 1266). Or the sometimes unnatural representation of the soundstage (while the hyper extended stage of the HD800 goes well with, for example, classical music, it doesn't necessarily fit equally well the most intimate jazz music - where the stage, in real life, is typically only a few meters long and not the tenth meters which an actual philharmonic orchestra takes..).