After several months of working on something else, I finally had some time to work on Group chat functionality. Focusing on something else was fruitful for me to solve this Group chat mystery. Once I started to work on it, the solutions just revealed.
Anyway Group chat is back. It works very similarly to Private chat, so every user has the group related messages in his own Message path. It means that everybody can control his own messages without touching the other users' messages.
The Group chat is only available as custom development. It's not part of the free version, and it's not part of the Premium version either. If you would like to use this feature, then please send me a mail.