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SpaceX Falcon Super-Heavies and gravity slingshots around Jupiter and the Sun could be used to catch up with the interstellar object. A space mission to chase down the Oumuamua object would be worth the $2 to 4 billion or so cost. Oumuamua is worth looking at for scientific value even it is only an anomalous interstellar object. Harvard researchers have calculated that unusual speedup and movement of Oumuamua indicate that it could be a solar sail.
The fast solar slingshot mission would be a very fast flyby. It would be better to brake.
Plasma drives are commercially available for station-keeping of Geosynchronous Satellites.
The Russian company Fakel has sold Stationary Plasma Thrusters (SPTs) for a couple of decades. The SPT-140D masses 8.5 kg, 4,500 W power, a specific impulse of 1770 seconds, a thrust of 0.29 newtons, and a lifetime of 4500 hours. The jet-efficiency is ~56 %.