flexible terminology / names

I would like to propose a flexible (ie configurable) terminology for companies, members, etc. to accommodate different types of organizations, such as companies, nonprofits, clubs or other associations, schools, and so on.

For example, ProjectPier might use a hierarchy of designations such as organization, group, and member. One could have multiple organizations; each organization has members and may also have group; groups consist of members who belong to that organization, and members can belong to more than one group.

When configuring a particular installation, the administrator would be asked to choose terminology for each kind of object. This is the terminology that would appear in menus and tabs. For example:
organization: company | association | club | congregation | firm | ministry
group: department | team | committee | task force | service | faculty | board of directors | senate
member: subscriber | associate | affiliate | employee | volunteer |

It would be useful to be able to specify additional characteristics, such as relationships. For instance, organizations can be clients, customers, suppliers, competitors, or partners of the master organization. Members also have relationships with the organizations and groups that they are members of. For example, department chief, committee chair, CEO, member-at-large. Clearly, since members can belong to both an organization and to multiple groups within that organization, multiple relationships can exist for any given member.