You could create a database for x conversations which contains all messages of these conversations. This would allow you to add a new Database (or server) each time x exceeds. X is the number conversations your infrastructure supports (depending on your hardware,...).
The problem is still, that there may be big conversations (with a lot of messages) on the same database. e.g. you have database A and database B an each stores e.g. 1000 conversations. It my be possible that there are far more "big" conversations on server A than on server B (since this is user created content). You could add a "master" database that contains a lookup, on which database/server the single conversations can be found (or you have a schema to assign a database from hash/modulo or something).
Maybe you can find real world architectures that deal with the same problems (you may not be the first one), and that have already been solved.
