Multiple passwords per key with any allowing decryption
You can do this by generating a (random) encryption key for the data and then encrypting that key separately with each of the passwords, using some password-based encryption.

To decrypt the user can use any of the passwords to decrypt the encryption key, then use that to decrypt the actual data. If the password-based encryption used is authenticated encryption, the decrypter can decrypt each of the encrypted keys and use the one where the authentication checks out.