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Imo the closest analog to a corporation is a program. It objectively exists like puppies do, but only when it's executed by the hardware, which are the people. Otherwise it's just a stack of documents without any real power to affect the reality.

You can easily guess what the purpose of the program is.

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Mathematical constructs like programs and theorems are a third category; they have structure and properties that don't depend purely on social construction the way a company's bylaws do. Of course which sets of axioms we prefer to reason from is socially negotiated, but once you've decided on a set of axioms, you don't have any freedom of choice about the consequences. This gives propositions about them a kind of objectivity that corporations or D&D characters lack. It can never be objectively true or false that a given corporation is, for example, bankrupt, but it can certainly be objectively true or false that a theorem is correct, or that a program performs an out-of-bounds array access when executed on the input "-0".

1500 years ago, Aryabhata came up with an algorithm for approximating an integer ratio with (what we today call) continued fractions, and we use it today for that and for inverting elements of finite fields. Aryabhata was a Hindu, speaking Sanskrit, living in a monarchy; no corporation he formed part of still exists, or could exist, at least according to accepted legal principles. Yet his algorithm continues to be correct today, and like the movement of the Earth, it would continue to be correct even if nobody believed it.

Platonists believe that mathematical constructs like programs are actually more objectively real than things like stones or puppies, because propositions about them have a truth-value that is independent not only of the speaker's social context but also of time. Today this puppy is alive; tomorrow she will be dead. The Pythagorean Theorem doesn't do that.

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