Append text to file without decrypting & encrypting again Is it possible to add a line to a file which is encrypted symmetrically or asymmetrically (private key refers to readkey below, public key refers to append key then) without decrypting it?

I was thinking about s.th. like:

msg1="hello"
msg2="world"
appendkey=...
readkey=...
file=touch(...)
addLine(msg1, file, appendkey)
addLine(msg2, file, appendkey)
ERROR=decrypt(file, appendkey)
WORKS=decrypt(file, privkey)

Then the WORKS equals to:

hello
world

The idea is, that various number of people can add s.th. to a file without seeing its content. Only the owner of the file can decrypt it once to see all lines (he/she should not decrypt all the lines individually for performance reasons). For me this scenario typically sounds asymmetrically, thats the reason why I thought that there could be a mechanism to use the public key to append s.th...
There may be a relatively straightforward answer, depending on your requirements: could you use a multipart MIME message with separate MIME sections, one for each user's encrypted contents?  

If you're looking instead for an asymmetric cryptosystem that supports appends, then maybe you can update your question to make that clear.