Seems that this once feature is no longer working again.
This is precisely what the CART function is for... allow someone to register multiple people for the same event... but not in a group.
When I try to activate this, when you click on the "add another event" and then choose the same event... the previous persons details are shown and saved.
I initially thought this was being caused by the cache being switched on... but no.
You have mixed up the concept. The add another event is for that user to register for another event. The only way to address what you are trying to do is to build a group.