What sort of messages? Unsolicited spam PMs? If so, one might be enough to get you banned. Don't exactly see how this relates to the topic at hand.
You are banned from posting or sending personal messages
So I thought there are some limits of sending message.
No question about Unsolicited spam PMs by the way.
Retina, you really need to read and understand the forum rules.
25. Ban evasion (using or creating accounts while one of your accounts is banned) is not allowed.[e]
25. If you get banned (temporarily or permanently) and create a new account to continue posting / sending PMs, it's considered ban evasion. The only exception is creating a thread in Meta about your ban.