What do I do if it's another person on my side of the negotiation that sent me a draft?

The new turn should be labeled as an "other" party - e.g., Other - Outside Counsel. If it's a new contract, simply upload that contract as a Third Party contract. If you have further changes to make on that draft and you want to deliver it to the counterparty, choose "redlines on top of redlines" in the export pane. This way, your counterparty will see your draft plus the prior turn.