My guess is that it depends both on the chef and on the 'concept' of the outpost restaurant.

It would seem that the most success would be had with a menu designed to honor the chef's 'brand', but that would be adjusted/enhanced to take into account locally-sourced ingredients.

Secondly, the chefs who will permanently be cooking at the outpost should be well-trained in the star chef's methodologies and philosophies, but should also be allowed some freedom to individualize the local menu.

I realize that what I'm describing is a hard balance to achieve.