In general galaxies in a group do not orbit each other in a tidy way like moons.
Relative movement is also very slow indeed - consider that Andromeda will reach us in about 4 billion years - to go around us in one orbit is over 6 times as far, so say getting on for 30 billion years, which is twice the current age of the universe, and then some. By which time most of the stars will have gone out!
Obviously things like the magellanic clouds are much closer, but even so it is wrong to think of them as looping around us.
But I guess there is nothing to stop you setting something up and giving them a nudge...