If 'oneness' is itself a form, then attributing oneness to every participating form generates a vicious regress parallel to the Third Man Argument Parmenides himself raises against Plato.

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Oneness(Contested interpretation: Fine (1993, 204) distinguishes Oneness from Uniqueness in reading 'each form is one'.): The property of a form whereby it is numerically or qualitatively one, derived from its role as the single entity 'over' many participants.
Parmenides: Parmenides was an ancient Greek philosopher (around 500 BCE) who argued that reality is unchanging and that change and motion are illusions. His radical ideas challenged everyday experience and forced later thinkers to reconsider fundamental questions about existence, making him one of the most influential philosophers in Western history.
Plato(the person whose decision to write is being analyzed in this example): An ancient Greek philosopher (around 428-348 BCE) who wrote famous dialogues exploring big questions about knowledge, justice, and reality.
Third Man argument(Platonic metaphysics / theory of Forms): A philosophical argument, analyzed by Vlastos (1954), that relies on at least three principles—One-over-Many, Self-Predication, and Non-Identity—and generates an infinite regress of forms of largeness, generalizable to an infinite regress of forms corresponding to any predicate.

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