I'm enjoying this thread.
I have this from a few perspectives, one is from a client who recently asked me "What does someone do with this much money" because he was a blue collar, fourth generation business owner staring at that much money. The second perspective is from someone who's trying to hire me and in this exact situation, either for his personal family office or in his business which basically represents private capital.
Financial Velociraptor is correct in that they mostly setup family offices, or have a fractional family office. That person is more of an employee and less of a money manager. The people who come into this level of wealth often have specialty skills/experiences in business and want to put that to use via direct investments into privately held businesses or real estate they are familiar with. A well run "family office" will have a chunk of their money in stock/bond investments, indexed or not, then have the rest for less liquid investments. Not necessarily hedge funds.
One basic example is the restaurant business. Notoriously risky, operator risk, site risk, trend risk, ect. I work in a city that has a significant number of wealthy individuals who made their money in the restaurant and entertainment space. If a young restaurant has 3-5 locations and a proven concept, they'll get "backed" by one or more of these family offices. The capital placement looks like a loan at 6% interest, then when its paid back the investors retain 10% ownership. The investors may also get the ability to be advisers as their hobby. This is all done with money that is above and beyond the family office's safety net.
Personally, I'm putting in just over a year above and beyond my FI number to have a small pool of money to hobby into alternate investments. For me, that'll be private placements with or through people I already know. Nothing concentrated, but a few $25,000 to $100,000 investments piggybacked with people I know will be enough to keep me mentally stimulated and engaged in business without it being a full time job.