Apple - Outlook 2016 Mac change order of accounts

I wanted to know the same thing. I searched and couldn't find an answer. I finally figured it out myself. You can change the "default" account and it will go to the top. Go to Tools, Account and then select the account you want to be the default. Click the gear at the bottom and select "Set as default."

Then, the remaining accounts will be put in alphabetical order. You may need to exit Outlook and reopen it to see the new order.

This works better than deleting the top account - letting the items shuffle and then adding the other accounts below since the sort order doesn't always follow the order of addition to the app. Especially if you have delegate accounts you're adding.

Also, you can identify the account inbox (and/or other folders) as favorite, which will move them to the top. Toggle (on/off) the star to the right of the folder in the main window. Version 15.36 (170702) moves non-Exchange accounts to the bottom regardless of default account.