Save and add new post

save_and_add_new

/**
 * Publish and go to add new post or CPT
 * @param  int  $post_id The Post id
 * @return void
 */
function save_and_new( $post_id ) {

    $cpt = ( $_POST['post_type']  !== 'post') ? $_POST['post_type'] : false;

    if ( isset( $_POST['publish'] ) || isset( $_POST['save'] ) ) {
        if($cpt) {
            wp_redirect( admin_url( 'post-new.php?post_type=' . $cpt ) );
            exit;
        } else {
            wp_redirect( admin_url( 'post-new.php' ) );
            exit;
        }
    }
}
add_action( 'save_post', 'save_and_new' );