[tennysont]

> without needing to modify your message

Careful. I argue this is even worse. In this convention, you need to change the behavior of others. If I send a message to Alice with contents "Hey, I can't meet today" using your sign-encrypt-sign scheme, then Alice can take the inner most layer and use it to impersonate me. Alice can send "Hey, I can't meet today" to Bob at any time. I must rely on Bob demanding proof that he was, in fact, the intended recipient.

From the first link:

> Note though that an effective security standard should require not only that the author must provide one of these five proofs, but also that the recipient must demand some such proof as well.

If your convention was upgraded into a protocol with automatic verification, then that would be different.