Cookie Error on new, third, domain

Hoi, I have a multisite installation with subdomains. I have a main domainname and one of the domains has it’s own domainname which works fine.

Now I want to set up a third domain for another subsite, but now I get the message:

Error: Cookies are blocked or not supported by your browser. You must enable cookies to use WordPress.

I get this message only at this new subsite, the old ones still work.

I tried adding
define('COOKIE_DOMAIN', $_SERVER['HTTP_HOST'] );
or
define('COOKIE_DOMAIN', false );

But that gave me a white screen with the message
The constant "COOKIE_DOMAIN" is defined (probably in wp-config.php). Please remove or comment out that define() line.

So can anyone point me in the right direction?

Maybe worth mentioning: Since my hostingprovider was taken over ny another company, my sites moved to another server a couple of weeks ago.