I'd say: Change the name (and update the Implementation section) and allow any of sticky and/or set?id bits to be set or cleared.  Most setuid programs nowadays are setuid-root, but there is nothing *wrong* with making a program that people can run with your permissions, it's just not very common.  All these bits, like the permissions bits, date back to the Sixth Edition and are the same in all Posix systems, despite their theoretical non-portability.