Add a class to posts in increments of 2

Filter post_class, use a static internal counter in the filter callback:

add_filter( 'post_class', 'wpse_100804_post_class' );

function wpse_100804_post_class( $classes )
{
    static $counter = 0;
    $counter += 1;

    switch ( $counter )
    {
        case 4:
            $counter = 0;
        case 3:
            $classes[] = 'extra';
    }
    return $classes;
}

In your loop template call post_class() like this:

while ( have_posts() )
{
    the_post();
    ?><li <?php post_class(); ?>>
    <?php /* more stuff */ ?>
    </li>
}