Let's suppose we live in different star system with two similar-sized planets (with a mass of three and a half Earths.) We live in Planet A, which is habitable. For some reason, Planet 2, our neighbor, enters in collision orbit with our Planet 1. But us, Planet-1ers are not happy with this, so we somehow catch Planet 2 and keep it close together. Both planets end up as a double planet.
Now, what would it take to catch Planet 2 and keep it orbiting along with ours? I'm aware that with current technology it is not possible, but let's suppose for a moment we have an advanced level of technology, but still not going off the laws of nature.