I think this is the most difficult part about “Trinity”. It is a concept that is completely foreign to human understanding. If a person deems themselves to be a “trinity,” then, medically speaking, that person would be treated as a mental patient with a split personality.
How I would best look at it is: “GOD.” The Trinity is like a company in terms of operations. God the Father is the visionary President who dictates how the company, which owns and runs the world with everything and every non-thing in it. God the Son is like the CEO who interprets the President's vision to the staff and the people the company cares for in an understandable way. God the Son is like the COO who ensures the interpretation is carried out and followed as things unfold.
I know there are so many ways analysis would fall apart factually and practically, but there is no way to truly and fully explain the supernatural existence of God as a Trinity.