This could be a problem with a cookie or a sed login:
As long as you he a cookie keeping you logged in to account #1, Outlook won't show the login screen and let you sign into account #2 until you sign out under account #1. If you had Firefox se your login for account #1, then you might not be able to access the login screen and sign in with account #2. To clear a sed login, you can use the Security panel of the Options dialog here: "3-bar" menu button (or Tools menu) > Security > Sed PasswordsIf you need to access two accounts on one website simultaneously, you might be able to use a regular browsing window for one and a private browsing window for the other. In a private window, Firefox won't use your cookies from the regular window. To open a private window, you can use the menu or press Ctrl+Shift+p.
Read this answer in context 👍 4