CORE allows you to set up clients with multiple email addresses and so you can send their invoices to multiple email addresses. When you have multiple email IDs for the clients, you can add multiple 'Email' contact methods to their profiles (Clients > Details screen). These need to be added as separate contact methods for the clients.
When you email the invoices to the clients from the Invoices screen, these multiple email IDs will auto-populate the To address field.
Note: If you have set up a Billing Contact for the projects in the Project Details > General > Details screen and checked the Send Invoice to Contact option, the invoices are sent to this contact instead of the default client contact. So you should make sure that you add the multiple email addresses in a similar manner to this Billing Contact in the Client Details > Contact screen.