Hi Jason Monroe,
May I first know which device are you using? Since the methods for different platform will be different.
If you encounter this problem on your iOS device, this may because that your iOS app is managed by app protection policies of your organization.
Typically, you will get such a notice: "The apps on this device are already managed. Only a single managed account is allowed on a device. Select account you want to remove. This account and all associated data will be removed from all managed apps.".
In this situation, only one managed work account supports to be used. The second work account will be removed mandatorily, it depends on which one you would like to use.
To sign in the account you want to use, you can first go to Settings > Sign out, and sign out the existed account. Then add another account back.
An additional personal account is also allowed, to add it: click the left top area in Teams, choose
Settings > Add account > Add existing account, then you are expected to add a your personal account.
If the above information will not be helpful for your situation, please kindly post back and provide us with a screenshot of the error page. So that we can help you better.
Best,
Shawn