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

rich! @ etiviti

rich

This plugin is perfect for private message spam prevention. It allows site admin and users themselves to limit exactly who can send messages to the user.
This plugin creates an admin settings page called Restrict Messages. Here the site admin can choose to impose global restrictions over who can send messages to the user.
If message restrictions are delegated to the user, a user settings page is created at Profile>>Settings>>Messages.
Each of these settings pages, depending on which is active, allows private messaging to be restricted to:
<ul>
<li>Friend Connections</li>
<li>Follow Connections</li>
<li>Groups Connections – with further selection of public, private or hidden status levels.</li>
</ul>
The public setting allows connections from all groups to send messages to the user, otherwise private or public stipulate only messages from these types of groups.
Once a restriction has been implements, the plugin removes the private message from the users profile, removes the usename from the compose message send to auto-complete and rejects any messages send where the send to includes an excluded user.
This plugin was originally created by Rich @etivite and is now supported by Venutius.
<h3>Extra Configuration</h3>

BuddyPress Restrict Messages

Exactly what I needed to improve a situation on a client site's, and lovely to see @venutius supporting and maintaining this plugin! Thank you!

Does the job!

This plugin allows the site admin to restrict who can send private messages or to enable the users to choose themselves.

Buddypress Messages Spam Blocker vs BuddyPress Restrict Messages