I've seen a couple of suggestions for ways we could theoretically catch it. One is high-Isp rocket motors, which I think would have to be nuclear-thermal like N

I've seen a couple of suggestions for ways we could theoretically catch it. One is high-Isp rocket motors, which I think would have to be nuclear-thermal like NERVA. If we had one of those already lying around, it might be possible to catch up. The other possibility I've seen discussed are extremely lightweight probes — chip-scale probes weighing less than a gram — accelerated by zillion-gigawatt laser arrays on Earth (or maybe in low Earth orbit). Since those probes don't have to carry their own fuel, they can reach much higher speeds, a sizable fraction of the speed of light, and could catch up to 'Oumuamua even if it took us a few years to develop the technology. Neither of those are technologies we have (though we did build and test some NERVA prototypes back in the day) but they are things that we, as a civilization, could plausibly develop.