Just a data point on actual usage of "enterprise" as "big org hq". (I'm not advocating this usage for our purposes, necessarily.).
From today's Fed News Radio e-newsletter:
NASA could be soon looking for another chief information officer.
Sources say Larry Sweet has told his staff he plans on retiring at the end of the calendar year.
Sweet moved to NASA headquarters from Johnson Space Center in June 2013 and worked for the agency for what will be 28 years in December.
Over the last two years, he has been advocating a concept called “enterprise first,” where the 18 space centers and organizations could take advantage of shared IT services.
Sent from my iPad
So I would tweak this to allow multiple purposes, with the caveat that the purposes should have appropriate synergy and not be a random grab bag. “Entities” that take on too many things become unfocused; however, too narrow a focus could hamper understanding context and addressing the large, but still focused, picture.
Lots of words are used in multiple ways ("overloaded" if you like) and this is one of them.
I've concluded that it's pointless to try to establish the "correct" definition for such words-- we are not the Academie Francaise, after all, or the OED; we can, however, decide how we will use the term in a particular document, report or whatever (and make that clear.) Or, rather than use really horribly overloaded terms, we can avoid them and pick another less popular term, and provide a nice clear definition in a glossary appendix.
With that preamble, I think a useful distinction I've heard in the discussion (e-mail and oral) in the SOA-RM TC is that "enterprise" should be used (in SOA-RM TC documents) to denote organizations (including joint ventures, associations, programs, temporary organizations) with a single purpose (and not merely "large" organizations, for example, despite my own first thought on the topic.)
If we adopt that ("common purpose") idea, then we should definitely state the definition in any document that uses it.