The experience of the British East India Company is illustrative.
The British East India Company started out administering small enclaves, usually around ports. These enclaves experienced dramatic population inflows from surrounding areas, based on the economic activity they represented and the fact that they were also generally better governed, even from the Indian perspective, than the surrounding areas.
In the modern era, central American states marked by corrupt governance are currently considering the establishment of such enclaves, as both an economic growth measure and a corruption-fighting measure, so it's not totally far-fetched to think that this could occur all over again.
The line between local administration and state power disintegrates quickly in such a scenario. Inevitably, there would be a lack of congruity between the company's administrative decisions (which begin to take on the character of judicial decisions) and the policy aims of the surrounding state. All it takes is one situation where the host power changes its mind, or tries to override an administrative decision it previously delegated to the company in its area, and the company decides to refuse the host's demands - and a new, micro-state has sprung into existence, in rebellion against the host state.
In the modern diplomatic context, of course, no other state would "recognize" the new state...unless and until it was victorious in its conflict with the host state. Diplomatic recognition tends to "follow the power".