I now have Outlook 365 and I can't find where it stores its files. I have been using Entourage 2008 and I know that all the data are stored in ~/Documents/Microsoft User Data/Entourage 2008 Identities, but I can't find the comparable location for Outlook. I want to know because, sometimes, I want to manually back up the data by copying to a clone (and I can do do that with Entourage). Any ideas?

Could it be in the Outlook package itself?

Have you tried searching for "Outlook" and "Microsoft" with Spotlight or EasyFind to see if anything that comes up looks promising?

There's a ton of stuff in there and nothing looks relevant.

Spotlight only comes up with the Outlook applications and EasyFind has myriad suggestions that can only be explored in geologic time.

In the meantime, look at this TS thread that I started.

Eyeballing your EasyFind results for all items that don't begin with either /Library or /System will narrow down your selection VERY considerably, I'd think, and what's left may be helpful.

I took a look at your TS thread and learned that command-shift-. (period) reveals and hides invisibles.

Nice idea about EasyFind, but still get a gazillion hits.

Outlook 2016 keeps it in ~/Library/Group Containers/UBF8T346G9.Office/Outlook/Outlook 15 Profiles/Main Profile
The individual messages are not files themselves. They are contained in an SQL database.

I had looked in ~/Library/Group Containers/UBF8T346G9.Office and there are three folders in each, namely Application Support, Caches, and Preferences. All these folders are empty. There are no hidden files there (I was able to show hidden files to check).

Time to call tech support?

Quite right. I'll post back with their information.