One file wants to belong to two users. How? Hard linking fails

Two setuid programs, /usr/bin/bar and /usr/bin/baz, share a single configuration file foo. The configuration file’s mode is 0640, for it holds sensitive information. The one program runs as bar:bar (that is, as user bar, group bar); the other as baz:baz. Changing users is not an option, and even changing groups would not be preferable.