Emails combined by Bill To customer?

I have been asked by several clients if there is a way to send one email per customer per invoice batch instead of separate emails for each.  Has anyone heard of a solution for this issue?

Example:  Customer 00-ABC has 5 invoices in the batch (could be different ship to addresses or could be the same).  With Paperless Invoicing enabled, they will get 5 emails.  Customer 00-ABC would prefer one email with 5 attachments (or a zip file) so my client turns off email for customer 00-ABC, prints the invoices to paperless, opens customer viewer, saves the invoices to her desktop, then attaches them to an email manually.

Would love to find a solution.