With a kind of hacking trick it is possible to run two Teams Desktops at the same time. First I need to point out that they won’t be running perfectly side-by-side all the time since some actions can affect the another one so this is not the perfect even when it is possible.
For example when you leave a meeting your another Team’s meeting might end as well. Teams desktop is not designed to be run with multiple instances so this kind of strange issues can happen. Of course it is important to remember that this is not backed up by Microsoft but there can be situations when you need to show another Teams Desktop UI when you are doing a Live Event/webinar or doing Teams training.
The steps to do this are in Tech Community post by Andrey Chekh.