Move from bare domain to www in multisite

We have a multisite instalation where our domain is set to a bare domain.

mydomain.com

We are facing a situation where we need to point use

https://www.mydomain.com as a primary domain.

Usually when moving domains i use the search and replace db script provided here.

Then i would also change the domain_current_site in wp-config to https://www.mydomain.com.

The problem is as soon as we make these changes we are having quite a few login/registration/possibly caching errors.

Is there anything with regards to the wordpress installation that i need to be doing?

Or am i doing to much?