Again, if we had the technology to do that it would be amazing.
We can't generate even within a couple orders of magnitude of the acceleration needed to do that.
We probably do have the technology (money is the hard part) to build a telescope array that spans the solar system, and to keep some rockets in standby orbits beyond Neptune. That would provide for earlier detection of an approaching object and a better chance of having a rocket close enough to intercept it.
The volume of space beyond Neptune is absolutely insane, and the speeds of interstellar objects (theoretical speeds that is, we don't have a large enough sample size to draw conclusions about how well that matches actual velocities) are also insane. We're very far from being able do this.
AFAIK, Japan conducted an experiment of asteroid exploration by collision and it revealed chemical composition. But if it's not an asteroid, it might be seen as rude.
There's a huge difference between doing that and doing it with an interstellar object going incredibly fast and extremely far away.
And if it shoots back, that’s briefly interesting too.
closest thing I read was one of these flying right between two fighter jets narrowly missing both, but also seemingly not course correcting or changing behaviour apparently.