I see nothing more than the intent to share knowledge of intent, or more concisely, to share intent. This can be reduced to a desire for synchrony of consciousness. When I sit down to play music with others, I do not have all of these intents and meta-intents. Yet it's arguably true that I do intend for the other musician to know that I intend him or her to know that I want to make good music. One can compose an infinite number of such statements concerning meta-intent and knowledge. But this is only an effect of the linearity of language, causing us to consider each constituent relationship one at a time. Beyond this, one can simply deal with the whole (jam session) in a highly functional, immediate, and mutually pleasing way.

Nth order desires are really just a variation on Xeno's paradox. It's a nifty mental exercise, but reality doesn't work that way. One just has 1st order wants, and a conflict resolution drive which is the only 2nd order want.