Sign internal emails as well

I got a request to not only sign emails sent to external recipients but also to users on the same mailserver, internal users.

The use case isn’t exactly clear yet but it seems to be primarily down to the little ribbon showing in Outlook. A secondary reason is the fact that the ribbon would proof that the email hasn’t been altered.

Is there any way to always apply S/MIME signatures no matter if a domain is internal or external?