Interesting question-- I'll bite:
In terms of an LLC's real estate matters, a Power of Attorney (POA) is usually redundant , because an LLC's flexible structure renders it moot. Your docs should declare who can sign what on behalf of whom, and under what circumstances, up to and including signing/engaging/burdening the LLC with obligations, debts, etc for Real Estate. ...and I suppose, as you said, up to and including authorization of a POA, I guess, but that's a pretty good-sized redundancy (or loop hole, depending on one's point of view.) Generally, if you need to 'fix' some internal process, you just amend your docs to include a scenario for signers.
Furthermore, the POA would generally be for the individual who's acting on behalf of the LLC anyway... so there's yet-another redundancy.
I'd contact a Corporate Lawyer for this purpose (and clarification!) At the very least, a Real Estate Attorney who has a sound Corporate background, assuming the LLC is a real-estate related entity.
This, I will say with some confidence: ALWAYS make sure that ANY POA drafted is LIMITED in person, purpose and time at a minimum. You don't want a blanket POA hanging out there to be acted-upon by someone at any time.
If you want to be more specific with your circumstances, maybe someone will be able to assist better.