You can add as many addresses as you like to your customer contact. You can do this while you are in the process of creating a new customer or going to the customer database to edit an existing customer's information.
Scroll down to the address section in your customer's profile tab. Click the '+' button above the current address(es).
A blank address field will appear. Enter the new address information as you normally would. You may add as many addresses to a customer as you need, by repeating this process.
Make sure to check the Set as billing box if this will be used as the billing address.
You also have the option to delete an address by clicking the three dots on the far right hand side and choosing delete.