What could be more obvious than that "a sufficient mass" would be most economically available from a small body with low gravity?Or that the acquisition of that mass would require less energy, as the original trajectory of said mass was closer to that of the asteroid you are trying to deflect?
Or that a piece of the threat asteroid itself would fill that bill better than anything else?
I only see disadvantages to attempt to steer the threat asteroid using a second, companion celestial object.
Even in the highly unlikely event that a small, companion celestial object exists near enough to the threat asteroid to be useful, it might not be detectable from Earth and its properties known at the time of launch. Moving two, small celestial objects in close proximity to each other, but allowing both objects to travel in free drift does not accomplish the objective with an acceptable degree of certainty.
Whatever tractor object is used (man-made or second celestial object), it must be propelled and steered intelligently to exert gravitational force on the threat asteroid along a constant vector over a very long period of time.
The success of the gravity tractor method, or any other method, to divert an asteroid depends on reducing variables and reliance on assumptions to an absolute minimum. If it doesn’t work the first time, we probably won’t get a second chance using the tractor method.
Reducing the celestial objects involved greatly reduces uncertainty. Keeping the threat asteroid intact in a single piece is critical. The “drill and nuke” method seen in the film Armageddon is fine for movie entertainment thrills, but not preferable in reality. It introduces numerous, unpredictable variables and creates intolerable uncertainty in estimating the number, size and trajectories of the resulting asteroid fragments and, thus, unacceptable risk of making the threat to Earth worse.
The gravity tractor solution has the elegant advantage of relying on a precisely known mass of a spacecraft and highly predictable gravitational attraction. The greatest remaining uncertainty in the tractor method is spacecraft navigation and long duration survivability. Both of these challenges can be overcome based on our prior experience and existing technology.