The best historical example is the British East India Company whose private army conquered India and ruled it for about 100 years. Another example is the United Fruit Company in South America that bought local armies to crush rebellions.

Since the US government has become so corrupt American companies have found it easy to use the power of the US government to coerce other countries, for example for intellectual property treaties. But it’s feasible that in the future companies might want their own military power to get their way.