This plugin allow you set quota for messages and conversations, so if user reach quota, he must:
1) upgrade membership status or
2) delete old messages/conversations
to send new messages/create conversations
Plugin Mailbox Limit allow you to set send limit messages/conversation in period, which you can also set, so you can set limit send 5 messages per day for user, if user reach limit, then he can send next messages tomorrow
Screen shots show mailbox messages only, is it working for chat too ?