Signed transaction must meet the signatory requirements setup based on the smart contract approval, etc... (thresholds, is the technical term).
Yes, our web interface will allow contracting parties to sign the transaction, we'll pass it along to the next party to login and sign the transaction envelope. Once all signers have approved/disapproved we'll either render them that the contract has fallen apart/doesn't meet requirements/could have been a disagreement, or we'll submit it to the network based on it meeting the threshold rules.
What I plan to do is route them and notify them over email that it's ready for signing. From my understanding as long as you have the XDR you can sign and pass around (still testing this theory) to the next party. I'll be making a blog post one of these days as I get into a bit more on transaction envelopes.
Edit: we would store the XDR, not necessarily route it around, just notify user we're ready for them to come approve it