Reshaping black holes to "push" the event horizon
The only places around one black hole where gravity would be strong enough to pull an object out from inside the horizon of another black hole are all inside the horizon of the first hole.

Remember that at minimum an object just inside the horizon of a black hole is traveling toward the center at the speed of light (as its speed would be measured from outside the hole, if we could see it) and getting faster. For a second black hole to catch up to the object to pull it out, it would itself have to be moving faster than the object - faster than light - which is obviously impossible but anyway would simply merge the two black holes, without rescuing anything.