> For example, I suppose two planets of equal size, orbital plane, and 180 degrees from one another would mute their gravitational effect on their host star.
Such orbits are extremely rare. Any such orbit would be highly unstable, as any perturbation would cause the planet to deviate from its location. (Strictly speaking, there are five points where objects can have an orbit that matches that of another planet. They're called the Lagrangian points, and the only ones that are stable are L4 and L5, 60˚ ahead and behind the planet in its orbit.)
Such orbits are extremely rare. Any such orbit would be highly unstable, as any perturbation would cause the planet to deviate from its location. (Strictly speaking, there are five points where objects can have an orbit that matches that of another planet. They're called the Lagrangian points, and the only ones that are stable are L4 and L5, 60˚ ahead and behind the planet in its orbit.)