exclude post from displaying in loop if it is in a category, but not in many categories

All you’ll need to do is count() the get_the_category() results to determine how many categories your post is in, and check it along with your in_category().

For example:

while ( have_posts() ) : the_post();    
if( in_category( $myCatsToExcludeArray ) && count( get_the_category( $post->ID ) ) == 1 ) {
do something
} 
endwhile;