Decrypting only message product - is it possible?
What's wrong with the obvious solution:


Each party creates a public-private key pair.
The public key is the combination of all public keys.
Encryption is done in a nested fashion to all public keys.
Decryption is done sequentially by all holders of key shares.


If some special property of a symmetric sharing scheme is desired replace the last two with
3. Encryption is done by creating shares according to the symmetric scheme and encrypting each share with a different public key
4. Decryption is performed just as in whatever symmetric sharing scheme was desired

Of course the size of the public key is linear in the number of shares. This is just the obvious solution not a great one.