in Royal TS, if you right-click on an active tab, you can then select "Duplicate (Ad Hoc)" from the top of the drop-down list. I believe that is the feature you are looking for.
Just to add to Germar's repsonse: you can also change the behavior of Royal TS when an active connection is double-clicked in the Options:
prior to Royal TS I was using ASG Remote Desktop. There I was able to just open a second connection to a server (e.g. putty shell) with just double clicking that resource. In Royal TS a doubleclick closes the session.
I could not find a way to accomplish that. What am I missing?