I'm not quite sure what you mean by an International School phagamas.
To me (& I am English, so this "taints" what I understand
) it would mean a school where nearly all pupils were the children of ex-patriot workers.
The subjects being taught would be to a curriculum & standard easily recognizable in my home country (although it could be based on the curriculum of any of the other English speaking nations)& any examinations taken would also be internationally recognised.
With the exception of Foreign Language lessons everything would be taught in English.
The standard of education would be recognised as to a fairly high standard even in my home country.
If that is what you also mean, then I do not think you will find anything like this in North East Thailand. Maybe in Chang Mai, but for the greatest choice it would have to be Bangkok.