[ QUOTE ]
Is it possible to get the CFII, MEI, and MEII add-ons all in one checkride?
[/ QUOTE ] Been there, did that, sort of. You can do them on the same day, with the same DE. You don't have to leave the room between the two orals, and you don't have to get out of the airplane between the two flights. Saves some time (introductions, paperwork, pre-flight, start-up, taxi, etc). Essentially, you don't get out of demonstrating any knowledge or proficiency, but it goes faster for all.
(note: DE's can only do 2 checkrides a day, an this counts as two).
As for teaching CFII in a twin without an MEI. I think we all agree that it's not a good idea (could get in trouble). The legality is questionable too.
My cut on it (just opinion) is as follows:
1. CFII: You've demonstrated your ability to teach and keep the plane flying in IMC.
2. CFI-SE: You've demonstrated you ability to teach and keep a single-engine plane flying.
But... You have not demonstrated any ability to teach and keep a multi-engine plane flying (even though you can fly one yourself).