From this answer, a MU site has the following in wp-config.php:

define('WP_ALLOW_MULTISITE', true );
define('MULTISITE', true);
define('SUBDOMAIN_INSTALL', true);
define('DOMAIN_CURRENT_SITE', 'www.example.com');
define('PATH_CURRENT_SITE', '/');
define('SITE_ID_CURRENT_SITE', 1);
define('BLOG_ID_CURRENT_SITE', 1);
define('COOKIE_DOMAIN', '');
define('ADMIN_COOKIE_PATH', '/');
define('COOKIE_DOMAIN', '');
define('COOKIEPATH', '');
define('SITECOOKIEPATH', '');

If I try to login to a child site @ http://example2.net/wp-login.php, I receive the error:

The constant “COOKIE_DOMAIN” is defined (probably in wp-config.php).
Please remove or comment out that define() line.

If I comment out:

define('COOKIE_DOMAIN', '');

I receive the error:

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

The site the answer above refers to is working with the definitions above.

Any ideas why the same definitions are not working on this earlier installed WordPress? (perhaps from around v4.3?)