Hi there,
This subject seems to confuse a lot of folks, here's my explanation.....
A solid state amp that works with high impedance headphones is a solid state amp that can put out a fair amount of voltage.
There is no real technical reason why a solid state amp should favour high impedance phones over low impedance phones other than the fact that it may not be able to supply enough current for low impedance phones or it has a very high output impedance.
If you have a solid state amp that can put out enugh current, enough voltage and has a low enough output impedance (i.e. less tha 5 ohms)then it should be able to work with just about any headphone regardless of headphone impedance unless you are using a super power hungry headphone.
There is NO MAGICAL IMPEDANCE MATCHING when it comes to low and high impedance headphones and amps.
Generally speaking you are looking for a desktop solid state amp, usually something with a fairly large power supply.
I have a Matrix M Stage, it has no problem driving my:
62 ohm AKG Q701
600 ohm Beyer DT880
2,000 ohm Sennheiser HD 424
Try reading this article, it may help:
http://www.head-fi.org/a/headphone-impedance
I hope this helps?
Chris