In addition to the Windows 10 Home and Pro editions; Microsoft also provides a volume license client for large organizations such as schools, governments and businesses who deploy Windows 10 in bulk, called Windows 10 Enterprise. With the release of the Anniversary Update, Microsoft has also provided an Anniversary Update for Enterprise licenses. The ability to upgrade Windows 10 Enterprise  will depend on your employer and Network/IT Administrators discretion. This is especially the case if you are connected to a workplace/school/domain.

How to upgrade to Windows 10 Enterprise 1607

Volume License clients such as Windows 10 Pro and Enterprise/Education utilizing KMS and MAK licenses should be updated by downloading the installation files for Windows 10 from the volume license servicing center.

If you have a MSDN subscription, you can also manually download the ISO from there then perform a offline upgrade.

If you are not connected to Domain, you should be able to upgrade to Windows 10 Enterprise using Windows Update.

If you are running the Long Term Service Branch version of Windows 10 Enterprise, you will be able to download the latest version October 1st, then perform a repair upgrade. Domain policies might restrict upgrades from occurring. Users can attempt the upgrade by logging into a local account on the machine. if you are unable to do so, its best you wait until your Network Administrator determines when your machine gets the upgrade.