Your challenge is to make a corporation so powerful, it actually has a de facto monopoly on coercion within a given territory. It cannot be acting at the behest of a state a la the British East India Company. The territory needs to be where it's base of operations is. It can relocate from a developed country to a developing country to achieve this, a la Kramer Associates. The POD should be post-1900 obviously. Bonus points if it manages to develop nuclear weapons.
How would such an entity function? What would it be like to live in?