How to invoice Woocommerce customer the remainder balance amount for additional items to an already paid order

I think you can detect order status change and store the current order total to be used as negative fee so that it can be deducted from order total before calculating total.

To make it less confusing the code should be something like this:

add_action('woocommerce_order_status_changed', 'add_credit_fee_if_editing', 10,3);
function add_credit_fee_if_editing($order_id, $old_status, $new_status) {
    $order = wc_get_order( $order_id );
    $order_total = $order->get_total();
    if($old_status == 'processing' && $new_status == 'on-hold') {//I am not sure about the 'on-hold' status's slug so verify that for yourself.    
        $order->update_meta_data( '_creditable_amount', $order_total );
    }
    if($old_status == 'on-hold' && $new_status == 'processing') {//I am not sure about the 'on-hold' status's slug so verify that for yourself.
        $order_credit = $order->get_meta('_creditable_amount', true);
        if($order_total > $order_credit) {
            $credit = -1 * $order_credit;
            $order->add_fee('Credit', $credit);
            $order->calculate_totals();
            $order->update_meta_data( '_creditable_amount', 0);
        }
    }
}

I think that this should work.