Alternative, more secure user registration process wanted
If you want to change the way a user can register on a Drupal site, I would rather implement hook_menu_alter() to alter the menu callback called when a user access user/register.

function mymodule_menu_alter(&amp;$items) {
  if (isset($items['user/register'])) {
    $items['user/register']['page arguments'] = array('mymodule_register_form');
  }
}


If you are going to allow users to enter an email that is already used from another account, then you should alter also the menu callback associated with user/register, as Drupal allows users to reset a password by entering their username or their email address.



function mymodule_menu_alter(&amp;$items) {
  if (isset($items['user/register'])) {
    $items['user/register']['page arguments'] = array('mymodule_register_form');
  }
  if (isset($items['user/password'])) {
    $items['user/password']['page arguments'] = array('mymodule_user_pass');
  }
}


The functions Drupal uses as form builders for those menus are user_register_form(), and user_pass(). You can use them as guideline for the code you implement.

Keep in mind the following points, though:


The unique email is necessary because Drupal allows users to request a new password by entering the email associated with their account. This is also helpful for who simply forgot their username, as the email sent from Drupal contains a link that redirects them to their account, where they will eventually change their password (or just enter their previous password to keep it).  
There isn't any security involved, as that doesn't allow a user to know all the emails used in a Drupal site, nor any email matching a partial email address. The users need to enter a complete email, and at that point there is few they can do; even in the case they try resetting a password, Drupal would sent an email to that email address, to which that user needs to have access. If that user can change the password of that email address, or can obtain it, that is not a Drupal security issue, but eventually with how that email address is handled, or who knows the password used for an email address.
If there is a security issue with allowing to use an email address to reset a password, then there would be a security issue even in the case the user is able to enter a username to request a new password, because somebody could find out a username already in use on a Drupal site.
Allowing to have not unique emails can create problems with modules such as the LoginToboggan module that allows users to log in entering their email address when logging in. There are probably other modules that assume there aren't two user accounts using the same email.
Enforce unique email addresses for users is a Drupal issue report related to what you are trying to achieve. If this patch is going to be applied, it will be possible to allow users not to have unique emails by setting the user_mail_unique Drupal variable.