Encrypt a file for multiple persons with different keys? I thought a problem and want to ask if there's a more elegant solution.

The scenario:
A company with a fileserver, which hosts encrypted documents.
The files need to be accessible by about a dozen employees.
Now the condition is, that each employee has different key material but all the employees can still access the file (even though they have different materials).

The most naive approach would be to give everyone the symmetric key that's it. This violates the condition.
The next way would be to store the file's key in a header, which is encrypted with each employee's symmetric key. The problem with this is, that everyone none can create new files without knowing the keys of the others.

The most optimal solution I'm aware of is to use asymmetric encryption to encrypt the file's key in a header for each employee using his corresponding key. This would enable everyone to create new files for the group and it would let everyone have different keying material (which can even be stored on a smartcard).

Now my question:
Is there a way to solve the above problem, without the overhead for the additional headers (maybe using some more esoteric protocol or algorithm)?

I'd prefer an answer which doesn't only give a name for the class of algorithms, but also instantiations, which are considered secure (based on blockciphers, asymmetric encryption schemes, ...)
Now the condition is, that each employee has different key material
solve the above problem, without the overhead for the additional headers

Based on your requirements - you must have the different key material for each user... which obviously has to be stored somewhere.  You don't want it in headers ... so it either needs to be in a different file / database, or in the meta-data.
We had a similar problem which we solved using Extended File Attributes instead of additional headers.  The symmetric file key was encrypted for each authorized recipient using the recipients RSA Public Key and the result was stored in the file meta-data.
https://en.wikipedia.org/wiki/Extended_file_attributes
Some filesystems have default limits on the amount of meta-data you can store. You may need to configure those.