When are officials no longer available for more assignments on the same day?

This is up to the organization to decide in their System Settings. By default, officials are only blocked out for just the time range of the games they're assigned to. So if you assign an official to a 10am-12pm game, they will be unavailable for any other games during that time since they are already occupied. You can change this setting, though, if desired in your System Settings under the System Defaults tab.  You can add some padding to that time to require a break in between assignments or only allow 1 assignment per day. 

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