All software has limitations. Depending on the version of Outlook, it can be 10-20, and is increasable via reg key. But that's only part of the issue, as caching/profile bloat quickly starts becoming a problem as the number of mailboxes grows.
Best get him to use OWA/the webmail instead. He can open separate tabs for each additional mailbox, add direct links to them as bookmarks or have them added to collections, etc.
Alternatively, setup forwarding so he can receive all (or at least some) of these messages addressed to these mailboxes directly in his own.