The Visual Studio integrated tool provided by Microsoft is fine but it's not enough for some rare scenarios in which we just want to add new tables (generate EDMX & C# model classes for just those new tables) to the existing entity model but not want to refresh the whole entity model (because the current EDMX is fairly much out of sync with what in the database and changing it a lot means testing is required a lot and I don't want that change).
It could have been an easy feature but looks like the only scenario they thought of here is a complete syncing (perfect mapping) between code model & database.
We can code to create such a tool but it requires fairly lot of efforts (regarding full understanding about the EDMX schema, the mapping rules, ...).
In the case where the model and the database are completely out of sync, it is more convenient to save the manual copying process, and add the mapping information from the content in the database to the EDMX file.
I am sorry that I have not found a similar software package in Microsoft that implements the described function/tool.