It is not possible to get the local IPs of computers behind a shared connection. Even if you could get them, they would not be unique, because they are reused - that's the whole point of NAT. You would have a lot of people using 192.168.1.1
or similar addresses.
If you want to differentiate between multiple machines that share the same IP address, you can add another factor, like the user agent string that tends to differ.
For example:
<?php
md5(
$_SERVER['REMOTE_ADDR'] .
$_SERVER['HTTP_USER_AGENT']
);
// 80b567b7c7ccfbda75a9712f16ca4429
would give you a hash that would only be identical if two users share the same IP address and have the same browser and operating system version.
Visit Panopticlick to find out more about "browser fingerprinting". Surprisingly, browsers are almost unique in the combination of their configuration. If you bring in client-side analysis with Javascript, where you can access display resolution, installed plugin versions and other details, you can easily differentiate between users that have a shared IP.