Hey Steve, sorry mate, missed this.
There's no way of limiting/setting the amount of conversations that members can have, this new system works fundamentally different to the old one. There's the ability to limit the amount of people in a conversation and we'll be looking at that in the near future. There are a few addons that can help out here but we need to look into them and do some testing if we're going to use one.
Thanks for that Tony, looks like we won't be getting any 'your mailbox is full' warnings any time soon then