How do I change or add to the email address which the invoice is sent to?

You are able to change the billing email address by logging into the desktop portal here and locating the Billing tab. You are then able to click the gear symbol next to the Payment Method to open Settings.

Underneath Email Address For Bills you are able to change the current email address or add new or multiple addresses.

Note that there is not an option to have no billing email address. To delete the sole address you would have to add a second and then delete the first.