I think I understand what you're saying.Yes, because their Trinity have common share the divinity from an identified deity, base on their illustration of Trinity in a triangle.
In which the three as distinct persons have their own sets of minds and different wills.
How do you see verses like this
Psalm 110: 1 <A Psalm. Of David.> The Lord said to my lord, Be seated at my right hand, till I put all those who are against you under your feet.
Do you see it as the father talking to the son? Something else?
If they have one mind, is a verse like that just for our benefit? Kind of a literary device?