quan_flo

If there is a user (or a bot) that signed up at your site this user can start to send messages to every other user. 
I had some negative experiences with this and so I wrote a module that should help to block such a spam.
Buddypress Messages Spam Blocker introduces some restrictions to your users:
<ul>
<li>New users can send messages only 24h after their registration, so you’ll have time if bot registrations have to be removed manually (modify this value using filter ‘buddypress_messages_spamblocker_newMembersWaitingPeriod’)</li>
</ul>
Their are also some more restrictions for mass mailings (mails that are sent to “friends” of the contact list are not included in this calculation):
<ul>
<li>Users can send 6 messages maximum in 5 minutes (modify this value using filter ‘buddypress_messages_spamblocker_5m’)</li>
<li>Users can send 10 messages maximum in 10 minutes (modify this value using filter ‘buddypress_messages_spamblocker_10m’)</li>
<li>Users can send 20 messages maximum in 30 minutes (modify this value using filter ‘buddypress_messages_spamblocker_30m’)</li>
<li>Users can send 30 messages maximum in 60 minutes (modify this value using filter ‘buddypress_messages_spamblocker_60m’)</li>
<li>Users can send 35 messages maximum in 12 hours (modify this value using filter ‘buddypress_messages_spamblocker_12h’)</li>
<li>Users can send 45 messages maximum in 24 hours (modify this value using filter ‘buddypress_messages_spamblocker_24h’)</li>
<li>Users can send 50 messages maximum in 48 hours (modify this value using filter ‘buddypress_messages_spamblocker_48h’)</li>
</ul>
Users with the capability “edit_users” (admins etc.) have no restrictions for outgoing messages
Install, activate, and it will work.
More about me and my plugins
Since the year 1999 I do administration, customizing and programming for several forums, communities and social networks. In the year 2013 I switched from another PHP framework to WordPress. 
Because not all plugins I’d like to have exist already I wrote some own plugins and I think I’ll continue to do so.
If you have the scope at forums or social networks my other modules might also be interesting for you. <a href="https://wordpress.org/plugins/search.php?q=quan_flo" title="ifs-net / quan_flo WordPress Plugins" rel="ugc">Just take a look at my WordPress Profile to see all my Plugins.</a> Use them and if my work helps you to save time, earn money or just makes you happy feel free to donate – Thanks. The donation link can be found at the right sidebar next to this text.

Buddypress Messages Spam Blocker

This plugin will block mass mailing for the buddypress messaging system

ckchaudhary

Extend BuddyPress’ private message feature by enabling attachments. This plugin enables users to send attachments in private messages. The type of file types allowed and maximum size of the attachment can be controlled by admin.

BuddyPress Message Attachment

Send attachments with private messages in BuddyPress!

Buddypress Messages Spam Blocker vs BuddyPress Message Attachment