Outpost has two ways to prevent your team from sending duplicate responses to the same email.
You always have the option to assign each incoming conversation to a specific member of your team - that way, your whole team knows who is handling which conversation, as shown below:
When you reply to a conversation in Outpost, the reply is considered a "draft" until the point when it's sent.
Outpost prevents more than one person from working on a draft at the same time. When another user is currently working on a draft, you won't be able to view or edit its text. Instead, you will see this message:
Once that user has sent or saved the draft, you will be able to access it again.
Incidentally, each user's involvement with the draft will be tracked in the conversation history, in reverse chronological order. Here, you can see that one user started the draft, and another user completed and sent it: