Multiple keys for the same ciphertext
In short: hybrid encryption.

Encrypt the content with a random symmetric key. And encrypt this key with the public key of each recipient.

Then all you need is a public key from all the people you want to share the content with. It doesn't even have to be the same public key cryptosystem for all the receivers.


  It might be they each come up with their own password or ...


Passwords alone are quite useless, and if you just use a password as key in a crytposystem, you screwed up badly. From a practical point of view, the concepts of a key and a password might be quite similar, from a security perspective they are not.

Of course you can design a system, where the users actually have to enter a password to decrypt their locally stored private key, like it is done for ssh keyfiles. But that is another issue.