Different layout on second page

To load override WordPress’ choice of template you can use template_include filter and then use the locate_template to return the the template file path (if it finds it).

The file-name passed to locate_template must be the name of the template file name (which should be in you theme/child-theme directory).

//Loads template customtemplate.php from your theme folder on page 2+ of the 'main page'
function my_second_main_template($template){
    if (is_home() && is_paged()){
         $alternate_template = locate_template( 'customtemplate.php');
         if(!empty($alternate_template))
              $template =$alternate_template;
    }
    return $template;
}
add_filter('template_include','my_second_main_template');