It sounds like a heretical understanding sometimes called PartialismPartialism, which suggested that the Father, the Son, and the Holy Spirit are parts of the one God. Partialism contrasts the The Athanasian Creed. Namely:
And the Catholic Faith is this, that we worship one God in Trinity and Trinity in Unity. Neither confounding the Persons, nor dividing the Substance.
And St. Athanasius writes in paragraph 28 of the Discourse 1 Against the Arians:
As we said above, so now we repeat, that the divine generation must not be compared to the nature of men, nor the Son considered to be part of God, nor the generation to imply any passion whatever; God is not as man; for men beget passibly, having a transitive nature, which waits for periods by reason of its weakness. But with God this cannot be; for He is not composed of parts, but being impassible and simple, He is impassibly and indivisibly Father of the Son.
In the Blue Plate special example, each portion is only part of the meal. Any one individual portion is not fully the meal. In the Trinity, each divine person is fully God.