We need to be able to create groups of students in which the members are private - not viewable by other students either in or outside of the group. Then we need to be able to send group messages and grant the group access to certain things. These would be groups created based on confidential information (disability status, for example), which is why the members need to be hidden.
Thanks for the feedback. Canvas offers the ability to separate students by sub-account, course, section, and group, each of which can limit visibility in some form or another. A couple of approaches have been outlined above that might satisfy the need to restrict student visibility in this particular way, so I will archive this idea. Additional comments welcome!