Validate and limit the user e-mail input to a specific domain name. WordPress.

wordpress_email_filter.php

<?php
//* Please do NOT include the opening php tag, except of course if you're starting with a blank file

add_filter('is_email', 'my_custom_email_validation', 10, 3);
function my_custom_email_validation($email, $submittedEmail, $context) {

  $allowed = array('example.com', 'otherexample.com');

  // Make sure the address is valid
  if (filter_var($submittedEmail, FILTER_VALIDATE_EMAIL))
  {
    $explodedEmail = explode('@', $submittedEmail);
    $domain = array_pop($explodedEmail);

    if ( ! in_array($domain, $allowed))
    {
      return false;
    } 
  }

  return $email;
}