In some CBs their lower XVs play in the main leagues, so I once checked to see if they were co-ordinating the teams. It looked as if they generated the fixtures for each league independently using their standard Berger Lite algorithm.But as crossref says we do not have coordinated fixtures for the different sides in a club so they can be heading to the four winds.
I suggested to the RFU Competitions people that modern software would easily solve the problem, but they weren't interested. Surely some major company must already have the programs and number-crunching facility to do a once a year run for all RFU competitions? Suitable publicity might even persuade them to do it for free.