Issue

Trying to active Microsoft Office for Mac 2016 a Macbook Pro. After entering valid Office 365 Business Premium user account login details following error message is displayed:

Another account from the same organization is already signed in

Resolution 

The issue was resolved by deleting all Microsoft related entries from Apple Keychain Access:

• Close all MS Office application
• Go to Finder > Applications > Utilities > Keychain Access
  Or just enter “Keychain” in Spotlight Search.
  
• Find and delete all entries that have a word “Microsoft” (and potentially “MS“) in both “Name” or “Kind” columns.
• Open MS Office and try activating your license again.

Microsoft Office for Mac 2016
Mac OS X 10.10.4