In the UK, they, to some extent, have lightweight racing trikes. Those are pretty well unknown in the US. The only upright trikes in the US are primarily intended seen as an old-person's ride, with the stability issues noted above. One of those trike manufacturers, Worksman, does in fact make a tandem trike. But it is a tandem version of a heavy upright trike, and not a 3-wheel version of a tandem road bike.

The arrangement above looks like lots of fun.