Authenticate Filter

I have two websites: one is a multi-site install, the other isn’t. On both installs, I have used the ‘authenticate’ filter to require admin users to provide an additional piece of information (via a custom form) during the login process. When this form is submitted, a custom code snippet validates the input. If successful, the wordpress function wp_set_auth_cookie runs (passing the User’s ID as a parameter) and then re-directs to wp-admin.

On both sites, admin users are logged in successfully. On the single site install, admin users can log out successfully from wp-admin but on the multi-site, the “are you sure you want to log out” message appears.

After many hours of checking and testing, I’ve been able to ascertain that the “logged in cookie” isn’t being set on the multi-site which is why the log out checks fail.

Do I need to do something different or in addition to wp_set_auth_cookie on the multi-site?

Many thanks