This is an awesome question. Going to take a stab at an answer, though I can't imagine a totally satisfactory one if you would rather not use "include" or "own." There are also some obvious answers that you can find in a thesaurus, so I'm going to try to offer some alternatives that you might not have considered.
Contains - From latin meaning "to hold altogether," contains might be the most appropriate if you don't want to use include.
Comprehends - Though now commonly used to refer to a cognitive understanding, this word is derived from the latin roots that translate roughly to "grasp together." The idea of being grasped or held together, as in a group, seems a nice blend of owns and includes. But be ready for many people to argue, "hey, that's not what the word means!"
If you chose, you could use the following sample sentences from a Google books search as evidence it was used in this manner. Note the dates, though.
The plan of the school comprehends an architectural or builders' course, a mechanical course, a course in freehand drawing, a course in cabinet work and decorative design, and a course in modelling. - From Annual Report of the Bureau of Industries for the Province of Ontario, 1893
The retail trade of the city comprehends every variety of store... - From Resources and Industries of the City of Lancaster, Lancaster, 1887
Houses or holds - I typically see this used when describing a collective in possession of another collective. E.g., "The city houses some of the nation's top institutions," "The county animal shelter holds some of the most desperate animals."
If you're willing to accept phrases instead of single words, I would also consider something like the following:
The church counts Fred as a member.
The club names Susan on its roster.
The group has claimed (or accepted) the individual as its own.