You can’t have different Edit Screens. You an only have one Edit screen and it’s permanently linked to the table.
A custom action could write special values to certain columns before opening the new screen. Or you could set up your custom edit screen so you fill user specific columns, and then add a button that writes those users specific values and special values to the existing row.
I don’t know that there is any specific documentation on “This Item”, but what you are doing there is essentially creating what’s commonly referred to as a Custom Form. To learn more about that, you can make a copy of the concept app in the below thread and study it.
Even though there is only one edit screen, you can set visibility conditions to the edit screen components to have one set show under one circumstance, and another set show under another circumstance. This won’t always be the best solution, but it works great in some cases.