You can apply a filter to comment_notification_text
:
1525 /**
1526 * Filter the comment notification email text.
1527 *
1528 * @since 1.5.2
1529 *
1530 * @param string $notify_message The comment notification email text.
1531 * @param int $comment_id Comment ID.
1532 */
1533 $notify_message = apply_filters( 'comment_notification_text', $notify_message, $comment->comment_ID );
If you have extensive changes to make, since the function containing that hook is pluggable, you may find it easier to replace the entire function.