I couldn't find much info on stacking the new ternary operator, so I ran some tests:
<?php
echo 0 ?: 1 ?: 2 ?: 3; //1
echo 1 ?: 0 ?: 3 ?: 2; //1
echo 2 ?: 1 ?: 0 ?: 3; //2
echo 3 ?: 2 ?: 1 ?: 0; //3
echo 0 ?: 1 ?: 2 ?: 3; //1
echo 0 ?: 0 ?: 2 ?: 3; //2
echo 0 ?: 0 ?: 0 ?: 3; //3
?>
It works just as expected, returning the first non-false value within a group of expressions.