Freemasons.
Wikipedia on becoming a Freemason: "The onus is on candidates to ask to join; while candidates may be encouraged to ask, they are never invited."
This directly contradicts what I had read years ago in some 18th-century document (I forget where, most probably French): I recall the document clearly stating that no one who asked to join could ever become a Mason, and that the only way one was ever inducted was to have led an exemplary life outside the organization. This would attract the Masons' attention, and then an invitation might issue. Asking without an invite would put you on the Masons' do-not-recruit list.
I somewhat like the latter better, because it seems to create positive externalities as well as an air of mystery. But I'm well aware that an unusually large amount of piffle has been written about the Masons, and I'm prepared to accept that it is false. Perhaps I will have to found such an organization myself, if one does not already exist.
I am not an expert, in my city, which is not very big, there are three lodges that I know, from different orders, I would say that it's a discrete society with different morals and ethics, freemasonry is not only one, there are several orders and branches, there are even imitators and liars with profit motives. Maybe some lodges can have dominant aspirations or something like that, I guess it would be necessary to investigate them from within or very close to get to know it but I don't think it would very far from churches or political parties with another kind of magic or mystery.
Its quite hard to say some thing you told great all about.
Hey @honeybee, I think Jack the Ripper was a Freemason. Is this the type of company your new organization is likely to be inviting?