There generally isn't any difference outlined between a CFI-ASE, CFI-AME or a CFI-IA. They're all CFIs and would generally make the same pay - assuming you had three people with only one of the ratings respectively. Most folks have all three anyway so ...
The majority of FBO's around here that I know of(NE Oklahoma/NW Arkansas) pay anywhere from $0-$10/hr more for multi instruction over single instruction. Most freelance instructors I know charge anywhere from $3-$5 an hour more. Instructors at flight schools in NW Arkansas were making 10-15 an hour, while freelance in NE Oklahoma/NW Arkansas are making anywhere from 20-35 an hour.
I've also seen rates change on the "level" of instruction. I.E. private -$20/hr, Instrument $25, Commercial $30 ... etc. but the instrcutor still makes the same regardless of the "level."
It really is such a varied thing. I know one airport that pays their instructors three or four different rates based on how many hours they bill in a pay period while the school across the feild pays $10/hr flat.