Send reminders based on invoice/product type?

Send reminders based on invoice/product type?

I have two types of products:
  • One is product-based and invoices are all individual.
  • The other is a service set up with auto-recurring invoices each month.
I have an auto-reminders set up to tell people when they are past due. However, when the service is past-due I would like to have some additional information like "Your service will be terminated if not paid, etc" to warn them ahead of time. But, I don't want this on all of the reminders since it doesn't apply to the product-based invoices - only the ones that are from the auto-recurring service-based invoices.

Is there a way for me to create an auto-reminder that is based on the type of product or invoice (recurring)?