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I purchased the pro version because I was very happy with the free version and I always have at least one other MySQL database to backup. the core vs pro chart says "Include extra MySQL databases in the backup set - core, NO - PRO, YES".

I do not see any method of including extra databases in the backup set. There is an option to backup "All configured Databases" but that sounds like it only backs up the databases and not the entire site. I'm stumped - How do I do a site backup and include extra databases? I have always been able to backup the databases separately via PHP MyAdmin, so an option that only backs up databases does not seem particularly valuable.

What am I missing?

The database only backup is for sites where the database changes quickly, but the files are relatively stable. It isn't an incremental backup, but it is the same idea. It works on some sites, other sites need a full backup.

You have to define the extra database from the Akeeba Control Panel. In the middle section, "Include data to the backup", select Multiple Databases Definitions. Once you have defined the extra database, it will be backed up with an "All configured database" or "Full site" backup.