Saving all values in “multiple select”

Answer 1

adding [] to the name was correct, however I allso needed to replace the following save line:

update_post_meta( $post_id, 'my_meta_box_select', esc_attr( $_POST['my_meta_box_select'] ) );

with the following:

update_post_meta($post_id, 'my_meta_box_select', array_map( 'strip_tags', $_POST['my_meta_box_select'] ) );

Thanks alot for the assistance Nate!