Could 2 objects of the same mass outside of an existing orbit create an orbit around each other causing a stand still?

I was thinking of the changes of how orbital motion has on objects of a varying mass, but if hypothetically an object of the same density, structure, and mass of the sun appear in our existing solar system would that object steal the orbital motion of the planets in our solar system? Or would the objects within our solar system lock in place due to a polar orbital pull. Wouldn’t this cause for each object to fight for the orbit of the other object, and could this create a pressure within space?

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Part 2; I am trying to change the binary star orbit, but to where both stars have the same mass. enter image description here

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