I had a thought… There are not many clowns. There is, in fact, only one. He is a timelord. As The Doctor and The Master took their names, The Clown did the same. Then he went out, into the universe, to make jokes and chaos.
It is clear that his TARDIS is a clown car (bigger on the inside, right?) If you see more than one clown together, he is crossing his own time stream for amusement. And, of course, since there’s a proliferation of clown sightings right now, something is about to be up.