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
Apparently it is coming soon. The Android app now has the ability to add multiple accounts to the app. This seems to have been with the most recent update. The desktop app, however, lags behind in functionality and that's where it needs to work like Discord or Slack. It's the only feature missing for me in an otherwise exceptional experience. For no, the android app is more capable than the Windows app and the web site.
As a Microsoft Partner that regularly signs up small businesses to Office 365, we use Teams to enable our clients to communicate with our support engineers. This typically means we have a user in each client's tenant that they can use to get ahold of us as needed. Cannot stress it strongly enough that being able to be logged into multiple Teams accounts at the same time, like we can with Outlook is critical.
Why the Android app is not feature equivalent to the iOS app is beyond me. The iOS and Windows apps can screen share but the Android app is not capable.