I have a simple set up - 1 main site and 1 network site.
I have got GSS working fine on the main site and also on the network site by inserting the following code into the wp-config.php file:
define( 'GLOBAL_SITE_SEARCH_BLOG', '1,2' );
On the network site, when there is more than 1 page of search results, clicking on the 'Next' page returns me to the main site and page 2 of the results.
For example, clicking on 'Next' from the network site:
will go to:
Is there a way to remain on the site you performed the search from?