Well as long as where on the topic of Islands/ Pacific ocean I suggest you guys look up the Failed Minerva republic.
tl;dr some Libertarian Millionaire found shallow reefs that no one gave a shit about and then when he did some shit a local ooga booga Island nation stole it and forced the people out.
We may be able to do the same thing but we would have to do it somewhere that isn't very close to any significant Islands, and we would have to bring guns so they can't straight up say "I'm da captain nuow"