Multi User Backup

On a tablet I have a situation where I have multiple users with multiple accounts, and I am trying to have the phone's state backed up in such a way that if I upgrade the operating system, every user's data is backed up. I would like to do this without imaging the phone, so that this backup can be applied to say, a newer version of the Android OS. I am ok with the backup being finicky, if there is some significant changes to the OS, so long as minor changes don't break it. I have tried Titanium Backup, and while it works perfectly for a single user, it does not work when multiple users are involved. Neither the user's, nor their data, is backed up. What application that can achieve this? Edit: To elaborate, backing up each user individually would work but it would be slow. We may be doing this on many devices, so this is primarily a way to save us time.