Being awarded a medal and having the right to wear it on a British military uniform are two different things.
I think the first question is 'has the Defence Council approved the wearing of the NATO ISAF Medal?' I'm assuming it has (not always automatic as they haven't approved wearing the NATO Article V Medal for Operation ACTIVE ENDEAVOUR) so the next question is which medal for which deployment.
If therefore one earns an OSM for one detachment and then goes on to undertake a second NATO detachment then I think there is a good case for wearing both medals.
As for awards given by another nation or earned on exchange - if one were to deploy to Afghanistan as an exchange pilot, say, then one wouldn't qualify for an OSM but would qualify for NATO's medal or indeed ones host nation's equivalent. But herein lies the snag. Wearing foreign medals requires special authority which is very rarely given, and almost never if one asks before it is awarded. Top tip, therefore is not to ask but pin on all the ribbons awarded and when questioned state confidently that Her Majesty personally wanted one to wear it because one is such a thoroughly good oeuf.