Hosting 2 WordPress websites in /public_html/ & /public_html/subdirectory/ at the same time

by

The problem was caused by:

define('DOMAIN_CURRENT_SITE', 'www.example.com/site3');
define('PATH_CURRENT_SITE', "https://wordpress.stackexchange.com/");

Changing this to:

define('DOMAIN_CURRENT_SITE', 'www.example.com');
define('PATH_CURRENT_SITE', '/site3/');

with a similar change in the wp_blogs table solved the problem.