Would The Philippines respect your sovereignty if someone bought one of the islands on the "margin" (remote)? Bet they would not,
I did not propose to attempt to take territory from a powerful, large state. The Philippines has a population exceeding 100 million.
bet they would not respect UN rulez (technicalitiez) re "stateless people".
The Philippines ratified it in 2011 after signing it 50 years ago. So apparently they are very much willing to abide by it. In my experience, the Philippines would. You could go on TV Patrol to garnish local sympathy.
It is (story link below) a British Overseas Territory, so might not be for sale. Would guess NOT.
The islanders are not desperate right now. You'd have to wait for the coming economic implosion. You could migrate there by the dozens and gain enough political power to help set policy, which I think is more realistic than trying to overtly buy them out in one move. The best would be a gradual infiltration and convincing (with money galore to help in the convincing). I could not accomplish that by myself. With perhaps 5 other like-minded guys and their extended families migrating there, we could probably accomplish it. The UK would fight us, but fuck them. As I explained earlier, there are limits to what they can do. Did you see the rape case on the island? The UK couldn't even put them in prison for a long time. The governor of the island was involved.
Looks kind of nice actually...
I would go crazy there. Especially they don't have fiber optic cable so the internet is atrociously slow (Tahiti has it some 1000 miles away). There is no way to land a plane there, so it is 3 days by boat to the nearest island that has air access (the other island under their nation could handle an airport but the UN declared it a private wildlife refuge

). The island is pretty damn small. Be okay if you like the people a lot and enjoy being around them.
I'd say if we could upgrade the infrastructure, and accomplish our goal, it might be worth trying?
We'd have to invest some time living there. We couldn't just waltz in and take over in one week. This would be a disruption to our lives. Is it worth it?
Also we'd really have to maintain the lives of the people there and what they love. I think they are essentially already anarchists, but they have some socialist needs.
One thing is the locals are not reproducing (youngest child is a 12 year old girl, next youngest is a 19 year old man) and many want to leave. So they would I think over time wither away in political control, if our offspring and immigrations were significant.
It is a lot of effort to undertake. I would not even consider it, unless I was sure we had a plan to outnumber the existing population.\
Edit: let me add that I am not interested to destroy the lives of the people there. I would only migrate there if I felt I could uplift their lives.