Elias here with Shopify Support. That's a great question!
I understand you're looking for a way for customers to add or edit to their existing orders, so your team doesn't have to issue extra invoices. Though there are a few third-party apps that can edit orders, there aren't many options that allow customers to edit their own orders. However, I was able to find one app that allows your customers to edit their own orders. Orderify allows your customers to edit their orders from their order status page and will automatically create a new order when they add or remove items. That way, it's similar to issuing a new invoice and allows the difference to be captured through the checkout. If you need any help with this app, you can also reach out to the developers directly through the contact information found in the Support Section of their app's page.
I hope this helps provide a solution to what you're looking for. If you have any other questions, don't hesitate to let me know!