Users can change the email id

On a self hosted WP, I am using google auth for a custom domain (gapps). I am using bouncer functionality in the plugin to allow only certain domains (gapps domain that I own) from signing in.

While this works for the first time sign -up, users can sign up using the gapps domain and then change the email id to any other domain ID which is defeating the purpose of the bouncer in some ways.

Is there a way to block changing of First Name, Last Name & Email ID for users who have logged in using gapps domain.