In that case you should not be working with the System.User entity but with a specialisation of System.User.
If your using the standard Administration module there will already be an Administration.Account entity and the included user management pages in that module will also work with Accounts. You can simply extend Account with any attributes you need there.
In a microflow you can always cast a User to its specialisation if needed.
You could retrieve the acount of the current user and make a reference from there to your site entity. Because that entity you can influance.