Q. Can I upgrade from Windows 10 Pro to Windows 10 Enterprise edition?
A. Yes and very easily (providing you actually have rights to use Windows 10 Enterprise edition). Windows 10 introduces provisioning packages which enable a new configuration, driver set, application and even SKU to be applied to another Windows 10 instance without losing the existing OS configuration, data, driver store and applications. This is one method to convert a Windows 10 Pro machine to Windows 10 Enterprise. Create a provisioning package that changes the OS SKU and key then apply (walkthrough is available at https://blogs.technet.microsoft.com/askcore/2015/11/23/how-to-convert-windows-10-pro-to-windows-10-enterprise-using-icd/)
Another option is to leverage the WindowsLicensing configuration service provider (CSP) which has the ability to change the edition as documented at https://msdn.microsoft.com/en-us/library/windows/hardware/dn904983(v=vs.85).aspx.
Another option is to manually run changePK.exe from an elevated command prompt and type in an Enterprise key and the OS will be converted.
A full list of all the upgrade paths and supported options is documented at https://technet.microsoft.com/en-us/library/mt605190(v=vs.85).aspx.