I suppose it depends a little bit on how your question is interpreted.

First off, the nature of the vast colonial-era great "Companies" of Europe and the relationship to their respective governments is quite complicated.

For recent standards, they had an absurd amount of power and very much operated as an extension of the state. Organisations like the East India Company (English) and the VOC (Dutch) obtained the rights/mandates/monopolies to seize territory and wage war in name of the crown or republic. These companies had armies and administered over territory.

However, if I am to interpret your question as "Could the VOC seize territory for itself and proclaim it as...oh I dunno, "Wonderland" and rule it as some form of corporate nation state?", then...no, not really. Certainly not officially. These Companies had so much power because they had the backing of a powerful nation. Going independant would undoubtedly cause 'friction'.

Now, when it comes to any territory being 'privately governed' in practice, that's an entirely different kettle of fish. It would completely depend which specific situation we're looking at, but there is no doubt that many people attained great wealth and influence from abusing their 'Company power' in rule and administration.