I wrote a simple function to perform an intersect on multiple (unlimited) arrays.

Pass an array containing all the arrays you want to compare, along with what key to match by.

<?php
function multipleArrayIntersect($arrayOfArrays, $matchKey)
{
    $compareArray = array_pop($arrayOfArrays);
    
    foreach($compareArray AS $key => $valueArray){
        foreach($arrayOfArrays AS $subArray => $contents){
            if (!in_array($compareArray[$key][$matchKey], $contents)){
                unset($compareArray[$key]);
            }
        }
    }

    return $compareArray;
}
?>