Can I add an additional status to the approval system?

GravityView has an internal system to approve or reject entries which can be used to control what's going to be displayed on the View. You can read more about that here: Approving or rejecting entries in GravityView

There's no way to change these statuses. 

If you need a different status, we recommend you add a drop-down field to your form with your own custom statuses:

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