Gamechanger on "Big issue with login"

Hello,
I try to run three sites with one wp instanllation.
My problem is, that I have big trouble to login the new sites, if I have define('SUBDOMAIN_INSTALL', false);. Also there is no access to any site, except the main page of the second and third site.
If I have define('SUBDOMAIN_INSTALL', true); I can access to the dashboard of the second and third site, but I am ether able to logout nor able to access with a new standard user.
The wp-config.php looks like this

define('WP_ALLOW_MULTISITE', true);
define('MULTISITE', true);
define('SUBDOMAIN_INSTALL', true);
define('DOMAIN_CURRENT_SITE', 'www.firstdomain.de');
define('PATH_CURRENT_SITE', '/');
define('SITE_ID_CURRENT_SITE', 1);
define('BLOG_ID_CURRENT_SITE', 1);

I tried many alterations from the wp multisite instruction, but nothing helped. What should I do to run these sites by not forcing to switch between Multisite true and false? Thanks!