How to Auto create Customer Site level Profiles

Summary

When a site is created, how to create a default profile class at the customer site level

Content

Whenever we create a customer and a site, we can see a default profile class is assigned at party level and customer account level. But at the site level, it always blank, we need to explicitly add the profile class.

Is there any way, we can automatically default the same profile class at site level too.

We need this functionality to send customer statements, (as we dont use statement site), for every bill to site, we have to add this profile class manually. Is there any way to auto asign the profile class at site level.