Elgg version?

Elgg version :  Release - 2.3.8, Version - 2016092300

1 - Override this view:

vendor\elgg\elgg\views\default\core\account\login_box.php

to add a new form\action

2 - For example, create a new form/action:

$body = elgg_view_form('connect');

Just copy login form/action and paste to same directories as connect form/action.

Read code to understand more.

3 - Unregister the exists action/login:

elgg_unregister_action('login');

And register your own custom action/connect:

elgg_register_action('connect', __DIR__ . '/actions/connect.php', 'public');

All in start.php of your custom plugin.

(You can use My plugin for Elgg 2 for that).

Server side solution:

server {

   ....

   if ($host !~ ^(site.com|www.site.com)$ ) {
       return 444;
   }

   ....

}

my_plugin does not show up in the admin/plugins applet.

Read this reply.

It's same for my_plugin.

Keep in your minds, this is a skeleton plugin and you must add your own cudtom views and make code.

Nothing works. I tried to use the start.php from the Front Page demo. I'm not sure where "$body = elgg_view_form('connect');" goes either. I give up. 20K users on our site are out of luck.   

Have you read the documentation on the links I mentioned?

Over and over. It's gibberish. All that was needed was to have changed the login path.

If you had installed Elgg 3 then I would have given you 2 lines of code and that's it. 

In your case, I need to take the time to write a few lines of code for you, create a few files and put them into a separate custom plugin. 

All you need to do is read the documentation and do as I wrote above.