Thanks Brajesh, you’re right. Checking against another site I’d used this on, the described behavior was not observed.
Is it possible I need to delete old tables in my DB Manager for the site in question? It was not configured immediately with the Multi Network plugin, but since its addition I have
1) deactivated BuddyPress on each subsite
2) added bp-custom with enable_multi
3) network activated Buddy Multi Network
4) single site activated BuddyPress on each subsite
5) gone to settings>BuddyPress and clicked “save” on each subsite
multiple times, in various sequences, however, I cannot get the groups to behave correctly. They do not all appear across subsites (so there is some “independence”), but they are being overwritten and the ID’s coming into conflict across subsites.