Multiple CSS body classes to specific page I.D.’s – is this possible?

I would consider making it more flexible by marking the pages in question with post meta or custom taxonomy. That way you don’t need to change a PHP code to choose what pages should have some custom look.

Here’s an example, if we mark the pages with the wpse-layout custom field with the value 1 (assuming there could be more layout options):

add_filter( 'body_class', function( $classes )
{
    // Only target pages
    if( ! is_page() )
        return $classes;

    // Get the 'wpse_layout' post meta value for the current page
    $layout = get_post_meta( get_queried_object_id(), 'wpse_layout', true );

    if( empty( $layout ) )
        return $classes;

    // Inject the 'wpse-layout-1' body class, 
    // if the custom field 'wpse-layout' has the value 1
    $classes[] = sprintf( 'wpse-layout-%d', $layout );

    return $classes;

} );

This could be further adjusted in various ways, e.g. with some custom UI.