"Is there anything likely to be at the center of a super-cluster of galaxies?"
Maybe we can say there could be a cluster which has a larger mass than the other clusters in the supercluster so that it attracts the other clusters itself. But it can't be any supermassive black hole.
First, we will need an enormous amount of mass so that galaxies can rotate around this mass. Let us think this idea, that may be a very very large black hole can do this. But we know that to create such a huge mass we need a star.
But as we can imagine stars should have a maximum mass limit to be stable. Hence we need a star that's so massive when it turns to the black hole it can rotate the galaxies around it. That not likely to be. Galaxies can have satellite galaxies but clusters do not turn around something.
On the Maximum Mass of Stable Stars.
Galaxies in the Superclusters don't need a massive black hole to stay together. They have DM and they are gravitationally bounded at most level.
But you might be interested in this,
The Great Attractor