Hello Jen!
I can see how saving all the email addresses you use for a customer in QuickBooks Self-Employed's would be useful. To send an invoice to more than one email address, you'll need to use the Additional email addresses field. I'm happy to go over the options with you.
Keeping things simple, QuickBooks Self-Employed allows you to enter one email address per customer. This goes in the Recipient's email address field and will stick with the customer, meaning if you create another transaction for this same customer, the last email used for them will automatically populate in the field. However, addresses you enter in the Additional email addresses field do not. The program also won't allow more than one email in the recipient's box at this time.
I can share your feedback about this with my team. We're always on the lookout for ways we can enhance what the program can do for our users like you.
I'm here if you need anything else!