I use Teams often in my voluntary work with Office 365 User group in DK.
I use Teams as a tool to interaction between my kids school (teachers/staff) and other parents.
I have three different(four actually, since I have a personal Office 365 account as well...) accounts and no option to be signed in to multiple accounts in the Teams app.
This means I am missing notifications and a smooth way of working, when having to sign in/out of the Teams app on my mobile phone. "Use a computer and different browsers" may be Your answer, but this is a challenge as well. First of all: I use my mobile phone all the time as a tool for fast communication, likes, chat and so on. Second: Company single sign-on usually gets in the way, meaning I have to use my browsers "private mode" to sign in. Luckily I am an IT pro, so I'll find my way, but poor fellow Office 365 users not as skilled within IT!
Small bumps on the way but not very productive, which is counter to Office 365 mission statement.
I am looking forward to the perfect solution (soon...). Thanks :)