Big Commerce - Add Delivery Days To Customers With An Account

We have a website built on Big Commerce.

We wish to add the following functionality:

We have customers who have an account number stored against their delivery address - these are known as account customers.

For these customers only, we want to add a drop down when they check out showing them their set delivery days. We will tell the system in the back end what days (Mon - Sat) the customer should see. They then select when they place their order.

When the customer chooses the day BC should associate a date for it and then the order export will contain the relevant date.

We would like to know if this is possible and for someone to set this up.