The center of mass of the solar system occasionally wanders up to 1/2 the solar diameter outside the sun. The sun rotates around this CM. Does something similar occur in spiral galaxies? If so, does a central black hole orbit around a galactic center of mass, or wobble? If so, can the effect be detected or measured? If so, would the central black hole collect more mass than if it were "motionless"?
Satellite galaxies like the Magellanic Clouds seem to me capable of supplying high non-symmetry that would enable a wobble.