As stated in the last update, the ability to use multiple Teams accounts at the same time is being implemented in stages for Desktop. Faster tenant switching functionality on the Windows client has been rolled out to the public ring fully, and Mac will begin rolling out soon. Work is in progress on cross-tenant notification improvements, and support for multiple accounts on desktop will follow. We’ll keep you posted!
Note: The ability to use multiple Teams accounts at the same time is supported on iOS & Android today.
Alex & the Teams team
I agree with @Bertie. To switch orgs is a very time consuming exercise AND what is really needed is that I can see activity in all the teams I'm affiliated to via my multiple identifications (volunteer groups, businesses, friends) without these "orgs" needing to be aware of the other "orgs". I should see and respond to the feeds without having to switch orgs just to see if there has been any activity.
Hope that helps refine the requirement.