I've found an plug-in for adding attachments to BuddyPress Private Messages. In 2012 an articles was published on WPMU: https://premium.wpmudev.org/blog/add-attachments-to-buddypress-private-messages/.
The plug-in isn't updated since 2012 and isn't working with Wordpress 3.2.1. or higher: http://wordpress.org/plugins/buddypress-message-attachment/
Since the plug-in is interesting for quite a lot of BuddyPress Developers (Downloads: 6000+), would it be possible that WPMU will update (futher develop) the plug-in?
It just a tip! The code is on GitHub.
For other users...please comment if you would like WPMU to update the plug-in!