That’s right! If your guest wants to add another day, they may request for an alteration. It would be best to send them this link since steps in doing this may vary depending on which device they are using:
https://www.airbnb.com/help/article/1420
Alternatively, you as the host can also initiate an alteration request. To do this, you may refer to this link:
https://www.airbnb.com/help/article/50
Either way, you'll get a notification to approve the change, allowing you to maintain control over the booking.