In Connexion client 2.63, opening the application with a right-click ensured that a new instance would launch, but in the 3.x version it just seems to switch to the already launched instance.
There has been a change from the earlier version of Connexion. It is not possible to open multiple instances of Connexion client 3.x / run multiple Connexion windows at the same time.
Workaround: Using the View > Pinned menu option within Connexion client will let you view records side-by-side or top-and-bottom when looking at multiple records at a time. Information may be copied between records in open windows.