Assume you have a vault containing secrets. Each one is encrypted for at least one authorized recipient using some public key crypto (one file per secret). Each authorzied recipient can decrypt all of those secrets. This implies that each recipient can also add additional recipients by decrypting all secrets and encrypting them again for the previous recipients and additionally the new one.
(The details of the encryption don't really matter here, for simplicity sake assume PGP/GnuPG is used.)
While this approach works well for authentication and confidentially, we have a problem with integrity. Malroy could easily add a malicious secret (i.e. a specially crafted phishing link) by encrypting this secret for all the indented recipients.
We could solve this by signing each secret or some kind of digest over the vault, but then we have to figure out who is authorized to sign a secret or the hash? How can we protect the integrity of our vault while still maintaining the ability to add recipients (authorized user)?