Skull and Bones and other, hidden societies

I'm sure you've all heard about Skull and Bones. (In)Famous group founded by Yale students/alumni which includes ex-Presidents, for e.g. George W Bush and his father H W Bush, John Kerry, amongst others.

Since 1982, the organization supposedly "went underground", as member roster lists stopped being made public, and the rumor is that there are MANY MORE people in power in the group now, and they continue to be very active throughout the 21st century.

No one really knows what the organization is REALLY about, or what its plans are, but speculation is that they are planning to use their wealth and influence in a collective manner to ensure that underground threats to USA and general humanity (secret nuclear plans, apparently) are stopped in time.

Anyone heard of this? Anyone has other speculations?

Also, what OTHER societies are there? Yale can't be the only one. IMO, if Yale has a mysterious alumnus society of power, so would Harvard and Princeton.

And by far, Harvard and Princeton do have more illustrious alumni with more diverse ranges of power...

I really want to know the validity of secret societal power monopolies.