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

BuddyDev

Brajesh Singh

shanebp

BP Messages Tool is a BuddyPress plugin.
By default, nobody can read a BuddyPress private message unless it was sent or received by the current logged-in member.
Occasionally, there is a need to respond to member complaints about another member harassing them via abusive messages.
This tool allows site administrators to review the messages of any member. They can also delete Message Threads.
NOTE: There is no UNDO for delete operations.
It provides a wp-admin screen available via Tools > BP Messages.
You can allow members to block each other by using <a href="https://www.philopress.com/products/buddyblock/" title="BuddyBlock" rel="nofollow ugc">BuddyBlock</a>

BP Messages Tool

This is a valuable tool which allows administrators to easily view user's private messages via the admin area. Tested and it works great!



Add some transparency to private messages

A good tool for BuddyPress

plugin is simple and does its job, the dev @shanebp is very responsive.

Buddypress Messages Spam Blocker vs BP Messages Tool