Thanks, that clued me in to the existence of superclusters, a term I’ve never heard before, and then I somehow wound up here in search of my answer of if the superclusters are orbiting each other. That’s a good read, for anybody interested, but here’s the summary:

One object orbiting another is an illusion. Instead, all objects orbit their common center of mass, called the barycenter. It looks like we orbit the sun because our common center of gravity is beneath the sun’s surface.

When it comes to galaxies, we can say that each one in a cluster, such as our local group, is gravitationally bound and orbiting a common barycenter. That means the Milky Way is orbiting a point in space roughly midway between here and the Andromeda galaxy.

At the scale of superclusters, however, the mass is too spread out and homogenous for centers of gravity to form. With no common center of gravity, clusters of galaxies have nothing to orbit and so don’t.

Instead, they are steadily pushed apart by the expansion of space.