Is there a way to create more Address Books?

I'm willing to organize my contacts in groups and the default address books -'Contacts' and 'Private Addresses'- are a bit restrictive to my needs (in fact, it don't seem possible to rename them, neither).

That would start out to be a Horde/IMP issue. Links to the Developer's FAQs are found in the SpamCop FAQ found via links at the top of this page.

Then it would be a configuration option that JT would need to be convinced to install. Just noting that one option of a 'group' address box was recently forcibly shut down due to one user's careless (ignorant?) action of using it, which then caused all kinds of concern about "who are all these people in 'my' addressbook which I did not create?"

Check the New Features Request Forum section and you'll find other additional features brought up dealing with the addressbook.

Thanks, Wazoo.

My first intention was to create address books (all private, of course) for 'Family', 'Friends', 'Work', and so on, to keep separated the addresses and make easier to manage and use them.

I will check the documentation that you have pointed me to.