Existing Other Person Conjugations
The wikipedia page on Grammatical Person, has this to say (emphasis mine):
Some Algonquian languages and Salishan languages divide the category of third person into two parts: proximate for a more topical third person, and obviative for a less topical third person. The obviative is sometimes called the fourth person.
The term fourth person is also sometimes used for the category of indefinite or generic referents, which work like one in English phrases such as "one should be prepared" or people in people say that..., when the grammar treats them differently from ordinary third-person forms. The so-called "zero person" in Finnish and related languages, in addition to passive voice may serve to leave the subject-referent open. Zero person subjects are sometimes translated as "one," but the problem with that is that English language constructions involving one, e.g. "One hopes that will not happen," are rare and could be considered expressive of an overly academic tone to the majority of people, while Finnish sentences like "Ei saa koskettaa" ("Not allowed to touch") are recognizable to and used by young children in both languages.
I think the grammatical persons of a language would be based on how the speakers of that language interact.
I would personally collapse singular and plural, and then think about what other possible persons there could be, adding fourth and fifth person conjugations as is fitting, but you could also remove a person.
No First Person
For example, you could have a heavy emphasis on an ego-less society, which would do away with the first-person. Pravic would refer to the
"me" in the third person, as
Or you could have a language with a strong sense of caste or class, where there are separate second-person conjugations for people in higher, lower, or the same class.