Yes some countries will allow children to retain dual citizenship and then surrender one of their passports when turning 18. Most EU countries and the US allow you to retain dual nationality, but in theory you should only travel on one passport, so flying out on one and back on another is naughty.
No reason why under certain circumstances folks couldn't have 3, anoyone in Northern Ireland can have dual Irish and British nationality, if thye married someone from another country and had a child the child could claim any of the 3 nationalities, certainly until it was 18.