The Perfect Arconym

Vicky Kalogera at Norhwestern posed an interesting challenge at Aspen last summer - is there a true 4th level acronym, and are there any perfect higher order acronyms?

So, a second order acronym, is an acronym with an acronym in it: thus LIGO is the Laser Interferometer Gravitational wave Observatory, and Laser is itself an acronym.

Then LSC - the LIGO Science Collaboration is a third level acronym, and something like the LSC Software Package - LSP, would be a fourth level acronym.

So, now the challenge: what "natural" 4th and 5th level acronyms exist (ones not just created to satisfy the challenge)?

Secondly, are there any perfect higher order acronyms. A perfect acronym is, of course, an acronym ALL of whose components are themselves acronyms. I can believe a natural perfect second order acronym exists, I'd be skeptical that there are any 3rd level ones (ALL the letters acronyms, all of which themselves are ALL acronyms).

For a more perfect challenge - consider TLAs only, or only acronyms which are proper words (aka apronyms)!

Further, there are recursive acronyms - the most famous being GNU.
But, are there any circular acronyms? I can't think of any, they'd have to be 3rd order or higher. An artificial example would be as follows:

consider FOO

FLAP is the FOO Logical Analysis Package

FUM is the FLAP User Module

and FOO is the FUM Object Organiser!

I'm sure better examples can be thought of.

Some time this week I may have occasion to think of science again. For now, indulge me, I spent 5 hours in meetings today, more than half of which pertained to a TLA Federal Agency. At least I refrained from using bullets...