What counts as portrait photography: one person or a group?

The Focal Encyclopedia of Photography includes an article by Kathleen Francis on the subject, which says in part:

Portrait photography produces pictures that capture the personality of a subject by using effective lighting, backdrops, and poses. A portrait picture might be artistic, or it might be clinical, as part of a medical study. Frequently, portraits are commissioned for special occasions, such as weddings or school events. Portraits can serve many purposes, from usage on a personal Web site to display in the lobby of a business.

One can find other more or less "official" definitions of portrait photography, but this one captures several aspects that are important to portrait photography (or to portraiture in the visual arts overall) which may not be explained in detail in a general-purpose dictionary.

A portrait:

• Captures the personality or essence of a subject. Not just a picture with a person in it. A "clinical" portrait might not attempt to reveal the soul of a person, but it still needs to capture something of that person's uniqueness — or else it's not a portrait.
• Is staged. While portraits can be candid, even those tend to have some intentionality. The lighting, backdrops, and poses are important, even if they are ad hoc. (Or maybe especially when they are.)
• Is commissioned. While this isn't necessary in a literal sense, in a larger sense portrait photographs are made for the purpose. Someone — the subject, or the artist, or some organization — wants a portrayal of a certain person (or group of people). Even a street portrait of a stranger can fit, based on the photographer's intention.

By the very existence of the term "group portrait", clearly such a thing exists. One can also say "individual portrait", but generally the implication of the term alone is that a single person is portrayed. However, if there are multiple subjects — the grandmother and granddaughter, for example — the picture isn't automatically a portrait without some of the above.

A successful photograph of a grandmother and granddaughter might be thought of as two portraits in one: first, a portrait of the grandmother, showing her personality through her relationship to the child; second and simultaneously, a portrait of the granddaughter, showing her personality through her relationship with the older woman.

A lesser photograph might succeed at just one of these, being effectively a portrait of one person with the other person as a prop. Or, if the focus is on the activity of the two subjects, or on their surroundings, it's probably not really a portrait.