Imagine a billionaire who is obsessed with the idea of running his own country. The size and geo location does not matter much. What matters is full sovereignty and international recognition.
Creating a new country from scratch, even with many billions of dollars, would take many years without guaranteed success, the main challenge being international recognition.
So the billionaire decides to approach a tiny but fully recognized and sovereign state with a generous buyout offer. The population size and the people living there are such that he is able to entice them all to take whatever sums agreed, relinquish any and all rights in the property and citizenship and go away forever.
Once that is done, the man becomes the head of his own country. He can rename it, create any form of government he wishes, any laws he sees fit, only allow people matching any specific criteria to visit or settle, etc. etc.
Would the above scenario be possible in terms of international law?