Multi-sig signature computation I don't understand, how multi-sig signatures are generated.

I've seen that inputs redeeming a multi-sig output, can be signed and signed over repeatedly, with different private keys using bitcoind's signrawtransaction, as it is done here.

But like this, the more and more signed transaction would need to be passed around among the different parties of the multisig.

Isn't it also possible to let the different parties of the multi-sig, individually produce their signatures, send them to one place, where they then are assembled to a scriptSig redeeming the multi-sig output?
Yes you are correct. The signatures are produced separately, by each signer and then combined into the final input script. When an individual is signing, he/she is not signing the a transaction with the signature of others, only the transaction sighash, where no signatures are committed yet.