The ISO could be coming in from any direction, in three dimensions, at any relative velocity to the sun, and with many possible perihelia and orbital elements. You'd have to detect it very far out from the sun so your statite would have the time to maneuver into the right orbit to start to make chase. The statites would also need to be on station far above and below the ecliptic plane for full coverage, very energy-expensive orbits.

There's another issue, which refers to an issue we brought up here recently, any orbit which is essentially static (not Keplerian) would require some tricky maneuvering, slingshotting and other gravitational tricks to set up. Sure, we could place a satellite in a static (non-orbital) location so that its distance high up the sun's gravitational well would provide the potential energy advantage needed to initiate a mad chase across the solar system after an ISO. Solar sails could be used to keep the craft in position with minimal energy expenditure, but getting it into that spot would probably be as energy expensive as our recent Solar Explorer mission we discussed a few weeks ago. See the comments for the following thread Latest Earth Flyby . . . by DanS April 11, 2020 3:14 pm

This project might make sense if you knew way ahead of time where, when, how fast and how close the ISO was coming, but to have a constellation of satellites in position to handle an approach with only a slight warning would be expensive. I expect it would require a constellation of at least dozens, and possibly hundreds, of statites, and this fleet would have to be managed, that is, launched, tested, maintained, exercised, and periodically updated and replaced as new technologies were developed and the birds wore out or became obsolete. And of course, the infrastructure to maintain this squadron (the "Mission Control") would be extensive and complex--much more expensive than a planetary defense system designed to ID and calculate orbits for potential earth colliders in the ecliptic plane. That's where we should be spending our money. Not only is the problem easier, it it has the potential for saving lives.

And how often do these outsiders buzz our solar system, anyway? We've seen only two over the last few years, but this could be just sheer luck. They might come through hundreds, or thousands, of years apart. We have no guarantee they are frequent visitors.

This sounds like just another engineering boondoggle to me: not necessarily scientifically impossible, just way too complex and expensive to be actually worthwhile.