Send and receive emails with wp_mail() for WP User (like Mailserver)

Sending mails from WordPress is pretty straightforward, using wp_mail. The tricky bit is receiving mail. You could probably achieve this by hijacking the method that WordPress has to post by mail. In that code you see this line:

do_action( 'wp-mail.php' );

This allows you to take over the posting process. So, in stead of posting the content of an email you could do something else with it, for instance store it in a table that is attached to a user’s profile.

Making this happen is likely a lot of work. Going with @Rup’s suggestion to use an external server is probably a better idea.