The Pro version of PublishPress Permissions does allow to you to create groups that work across all the sites in the multisite network.
You can enable this feature by going to Permissions > Settings > Network in the main site on your network.
After this is enabled, your groups, and their user membership list, will become available on all sites in the network.
It is important to understand that these groups do not automatically grant permissions network-wide. Extra roles and Specific Permissions are still set per-site.