<?php

$args = array(
	'post_type' => array( 'type1', 'type2', 'type3' ),
	'posts_per_page' => -1
	);

$myquery = new WP_Query( $args );
	$type1 = 0; $type2 = 0; $type3 = 0; $count = 0;
	while ( $myquery->have_posts() ) : $myquery->the_post();

	if ( $post->post_type == 'type1' ) $type1++;
	if ( $post->post_type == 'type1' && $type1 > 3 ) continue;

	if ( $post->post_type == 'type2' ) $type2++;
	if ( $post->post_type == 'type2' && $type2 > 3 ) continue;

	if ( $post->post_type == 'type3' ) $type3++;
	if ( $post->post_type == 'type3' && $type3 > 3 ) continue;

	$count++; if ( $count > 9 ) continue;

	// Do Stuff

	endwhile;

?>