If you want real expertise on this kind of question, you should attend “Social Ontology 2018, the 11th Biennial Collective Intentionality Conference” from August 22-25, 2018 at Tufts. But in case you want some light musing on the subject …
A system is an assemblage of interacting parts that persists over time. It can change, but a parsimonious description applies over its whole history. (“My Mac could run SPSS once I installed the new software, but it’s still the same system.”)
An organism is a system that no one designed. Instead, it results from the reproduction of similar organisms.
A biological organism is an organism that exhibits the properties of life. This definition implies that there may or could be non-biological organisms.
A sentient organism is one to which we can accurately attribute mental states, such as pain, pleasure, aversion, desire.
A person is a system whose mental states include memory, planning, and decision. Thus the person’s development over time is partly her responsibility, not solely the result of accident and force. Not all persons are organisms. Entities that meet the definition of persons include human beings but also God, angels, devils, space aliens, perhaps other advanced mammals, perhaps some future AI, and organizations–see below.
A human person is a person that is also an organism of the species homo sapiens. A human person is capable of certain specific mental states that are not necessary conditions of personhood in general, e.g., love and suffering.
An institution is a system composed of at least two persons, plus any number of other components (e.g., buildings, legal rights). A market, for example, is an institution that combines many buyers and sellers, their goods, their rights, rules, and so on. Note that a market is not a person because it doesn’t have mental states.
An organization is an institution to which we can attribute memory, planning, and decision. Such attributions are not metaphorical but use exactly the same logic that we apply to human persons. (“I can tell that Tufts intends to educate students from the fact that it expresses this intention on its website and then actually educates.” Tufts doesn’t love, but Tufts does intend and plan. As such, it is a person.)
By these definitions, a social organization is a person; it is simply not a human person. It lacks the rights of a human being. Human beings gain rights not from the mere fact that we are complex systems capable of remembering, planning, and deciding–so are organizations–but from something else. I would attribute our rights to the fact that in addition to being able to remember, plan, and decide, we can also love and suffer.
(I was led to these thoughts by the discussion of Elinor and Vincent Ostrom and their eclectic readings of Daniel Dennett, John Dewey, Douglas North, and others, as summarized in Vlad Tarko, Elinor Ostrom: An Intellectual Biography, pp. 137-43. See also: against methodological individualism; why social scientists should pay attention to metaphysics; and the legacy of Elinor Ostrom and the Bloomington School.)