A flower is a being with no person. I am a being with a person. Suppose maybe, in some alternative universe, there is a being with three persons. We have difficulty imagining this, but in a different universe on a planet with a nature completely different than ours, it might be possible.This, to me, does not seem too outlandish, especially if we conceive these creatures as developing by a completely different process than our biological procreation and growth. Now, suppose we consider God, who is the very ground of all being. He might have much higher capacities for personhood than we can conceive of or are used to coming in contact with.
Or, rather than thinking of “being,” we could think of some kind of trope theory. As Brian Leftow said:
“[…] there is just one divine being (or substance), God….[As Thomas Aquinas says,] God begotten receives numerically the same nature God begetting has. To make Aquinas’ claim perfectly plain, I introduce a technical term, “trope”. Abel and Cain were both human. So they had the same nature, humanity. Yet each also had his own nature, and Cain’s humanity was not identical with Abel’s… A trope is an individualized case of an attribute. Their bearers individuate tropes: Cain’s humanity is distinct from Abel’s just because it is Cain’s, not Abel’s. With this term in hand, I now restate Aquinas’ claim: while Father and Son instance the divine nature (deity), they have but one trope of deity between them, which is God’s….bearers individuate tropes. If the Father’s deity is God’s, this is because the Father just is God.” (1999, 203–4, original emphasis) 
Please share any thoughts in the comments. I would love feedback .