The Big Four are indeed organised as groups. A headquarters entity (three in London, but KPMG is instead based in the Netherlands) owns the name, and then hundreds of notionally independent companies in other countries around the world use that name under license (for a fee and other conditions).

In practice obviously that headquarters organisation has considerable control, and key people merrily teleport from one "independent company" to another over their careers.

The appropriate word to describe them is probably "corrupt". If I can have two words, how about "very corrupt" ?