Can I set a custom response cookie on a signOut response?

[lorenzo-dallamuta]

Is there a way to set a response cookie on the response of /api/auth/signout? My need is that at signIn I'm forwarding the Set-Cookie header from a Drupal backend through the Next server to the client and i would like to do the same for the logout, but the signOut event, as far as I understand, does not allow to set a customized response.

Edit:
in fact, it'd be also useful to be able to send the cookie back from the browser to the Next backend somehow at sign out 😅