What I have successfully done is this (VB.Net).
- make updates to the database as desired/ required
- Choose "Update from database" in the EDMX model, the graphical model will correctly show the new structure/tables
- Expand the project so that it shows all related files
- The two files with the "tt" extension are the ones that matter: first take the one WITHOUT the .Context. before the tt extension. right click on it and choose Run Custom Tool:
- Do the same for the .tt file with the .Context. in its name. All of your code and logical model classes will be updated.