Well this can be achieved by adding these lines somewhere in levelup.php:
PHP Code:
$result = runquery("SELECT * FROM {$prefix}vote_voters WHERE adoptableid='{$id}' and date = '{$date}'");
$num = mysql_num_rows($result);
if($num >= 10){
$article_content .= "An error has occurred, this adoptable has been leveled up 10 times already today. "
}
else{
// codes to execute if the adoptable can be leveled up
}