Editing the availability calendar follows the same steps regardless of whether or not you have game assignments.
However, if your officiating organization uses the Availability Locking feature, they may limit your permission to edit your Availability Calendar once you've received an assignment. It is up to your officiating organization (i.e., your scheduler) to decide whether they want to allow you access to change your availability after receiving an assignment. Each organization can choose whether or not to turn this feature on or off. You must contact your organization for further information on which decision they've made and why.
You can read more about the Availability Locking feature in this support article.