Search pre_get_posts filter which can handle multiple post types and categories?

Question

I have a Search which allows users to search multiple custom post types (CPT). That works fine. BUT I would like the query to exclude specific tags from each of the CPTs.

Eg. Include ( (Posts excluding category X) AND all CPTs of post_type 'doc') which have the given search term.

I know how to do this with a new WP_Query object using taxonomy $args... or a plain SQL query but I can't figure out how this would work with $query->set().

Perhaps there is a way to supply a complete taxonomy array... or a raw SQL query?

add_filter('pre_get_posts','SearchFilter');
function SearchFilter($query) {
  if( ! is_admin() ) {
        if ($query->is_search) {
            $aPT = array();             
            if ( isset($_GET['include_docs'])  )
               $aPT[] = 'docs';    
            if ( isset($_GET['include_general']) ) {
               $aPT[] = 'post';
               $aPT[] = 'page';                
            }
            if ( isset($_GET['include_nl']) )
               $aPT[] = 'newsletter';              
            $query->set('post_type', $aPT );    
            $post_type = get_query_var('post_type');
            if($post_type)
               $post_type = $post_type;
            else
               $post_type = $aPT;

            $query->set( 'cat', '-7,-19' )  // should only apply to posts not cpts
        }
  }
 return $query;  

Answer 1

You can set tax query in pre_get_posts hook as well:

$query->set('tax_query', array(__standart parameters__));