I just found out about the Comet Interceptor - designed to remain parked in space, ready to fly to a new target at short noticehttps://interestingengineering.com/innovation/esa-mission-la... - but it's not the same as a few like that being already in motion and between slingshots at different corners of our system (if something like that could be at all possible..)
If you want to intercept something that will quickly leave the solar system you have to get on a trajectory that will quickly leave the solar system. And you have no idea of what the correct plane will be in advance.
I wonder what range of velocities you can sustain and how close to planets (suns) you can come to catapult or slow down to stay in the system (starsystem) moving fast, and how many jumps for how many probes moving such fast would be needed to at least be able to pass by visitor/suspect at some point or time really close even if not matching speed or direction.