Mail application for a private group?

Does Yahoo or any mail system allow a mode similar to WhatsApp?

That is, two (or more) people to be able to exchange emails they must first agree by forming (or joining) such a "private" group.

The mail system otherwise **should not even deliver** an email and should send a non-delivery message (such as "the mail could not be delivered").

The recipient may or may not want to know of such an attempt, or may want to know the first time so the sender can be "registered"

The current Yahoo "block sender" still delivers the mail albeit to a junk folder. What is being asked for is not to deliver the email and send a non-delivery text. 

Why the question? Someone I know get persistent, obscene emails from a sender. Complaining to police stopped this for a while but resumed after an year or so.

Changing email address is not an answer. Because is is not difficult for someone to get hold of your address and also you have to communicate the change to a large number of genuine friends

Other practical suggestions also welcome -thanks  

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