Adding cost to existing order after payment

I am running Woocommerce 3.x. I would like to have the option, to charge additional costs for an order after payment for it is complete. I realize you can change the order if placed on hold status. However adding additional cost and sending the invoice does not return link to pay the additional fee. Is this even possible, and if not? Is there any possible workaround this option.

Sending client the additional fee as separate order forces the order to be automatically completed, which in return generates emails what are extremely misleading for the buyer. Which would work as an option, if I was able to force for the order not to send any emails out.

So, in the end, the question is. Can I send additional payment page link to the client, where the buyer would need to pay the difference, on the same order? Or is there an option to force order to not send the automatic emails to the buyer?