Someone I know is going through the process, well her children are and then the grandchildren, they are all USC's but can get a EU country passport through her.
Much easier if get it all sorted out when they are younger.
They keep on saying they are getting their citizenship, they are of course citizens but are unknown to their mother country.
I did meet a guy years back who had 6 Citizenships, I am sure that will not be the record.