The Private Messages Limits module allows you to set a limit for the number of privatemsg module messages that can be sent per period of time.
An example with the following settings:
- Messages per user: 5
- Period: 20 min
- Warning level: 3
User hasn't sent anything in a while, they go to create a new message, enter 2 names as recipients, and then click send. 5 minutes elapses and they want to send another message, when they go to the form, they get a message that only 3 messages remain, but that they will get new messages in 15 min. This time they enter 3 people and send. 5 more minutes go by and they decide to try and send some new messages. They go to the form and they get an error message at the top saying they have no messages left, but that in 10 minutes some will expire. Right now, they can still try to fill out the form, but they will get another error (same as if they had tried to send to 6+ people in the beginning).
- has a patch (module) for privatemsg that would allow for limiting inbox sizes.