Strangely, I think the K550s sound even better through the E11 when the E11 is connected to the E10. So long as the E11 is plugged into something that already sounds clean, the E11 is really good if you are wanting more volume. The best thing about the E11 to me is the fact that it boosts the really low end bass. Nothing else I own boost the bass as nicely as the E11. It could just suit my K550s and ATH-AD700s. The E11 works out better in many ways than the E10, It goes quite a lot louder as well as having a deeper and more powerful bass boost. I think the E10 does sound very good but better without the bass boost most of the time. The E11 seems to make the treble stand out more than the E10 does too. Most noticeable when high gain is on.
Something like the E11k or maybe a second hand E11 would be a good choice (so long as you plug them into something that already sounds reasonable). From what I have heard, the E11k sounds like it boosts the really low sub bass. I bet the K550s would sound great with a little bit more weight to that. I think that is what my E11 does already so I don't need to get the new version. I don't really like the style of the E11k anyway but that won't affect the sound in anyway.
My E11 never makes the sound quality of anything down and having such good bass boost on it is a bonus. I find it useful a lot of the time. I use it at my desk in the line out of my E10 and I also sometimes use it strapped to the back of my FiiO X3, yet again because the way it boost the bass suits my K550s a little better that the X3's bass boost does.
I even use the E11 though the line out of my Pioneer stereo amplifier as the headphone socket on that doesn't sound as good as the E11, although it is much louder.
Sorry, but I think I talk about my E11 too much!

I think it is my favourite FiiO amplifier for the money. Many of FiiO's headphone amplifiers will do a good job of giving you more weight and depth to the bass with the K550s. Most of the time, I just use my FiiO X3 with the K550s with no extra amplifier and just use the built in hardware bass and treble controls to suit my needs. I would use the E11 if it didn't add so much bulk to my X3.
The E10 is only really a desktop amplifier as it has no battery and both the sound and the power goes through the USB cable to the device. Only really useable on a PC or laptop. FiiO do have a lot of different amplifiers if you have a look on their page.
http://www.fiio.net/en/products