E.g. N parties show up in a communications group and want to make a joint transaction. They each name an input they want to spend and signmessage for a zerocoin creation showing that they have the authority to spend that coin.  They then return anonymously and provide zerocoin spends that specify the outputs they're interested in. Everyone then knows what the final transaction should look like and they all sign.

In this case the zerocoin part is used to prevent parties from jamming up the mix, e.g. by joining and providing inputs but refusing to sign. If someone refuses to sign— it can only be because either zerocoin has been exploited (and their preferred output isn't in the mix) or because they're trying to jam it.  In any case, you just blacklist their input, and restart the process. Because zerocoin is only used for anti-dos in that context it also means that you could use a faster reduced security instance of it, also allowing some experimentation with the security boundaries.