On multisite the object cache prefixes keys with the current blog id, so the same key on two sites does not collide. Some groups must not be prefixed — users exist once across the network — and those have to be declared.
wp_cache_add_global_groups( array( 'my_plugin_licences' ) );
wp_cache_set( 'licence', $data, 'my_plugin_licences' );
// same value on every site in the network
Getting this wrong on a single site has no visible effect, which is why it is usually discovered when a plugin is first installed on a network. The declaration has to happen before any use of the group, so it belongs on init at the earliest priority or in a drop-in. There is also wp_cache_add_non_persistent_groups() for data that should never reach Redis or Memcached.