The partially signed raw transactions are not stored on the blockchain or automatically transmitted between nodes. These are simply data structures that are built via MultiChain's APIs, and nothing happens on the blockchain until the final sendrawtransaction.
So if you want to pass a pending transaction from one user to another, you either need to do it off-chain, or else do it explicitly on-chain using something like a stream (the transaction can just be the payload of a stream item). But in the latter case, you should be aware that all nodes will see that partially signed transaction.