Fishing is fourth profession, and it means wandering empty space and gathering matter. I imagine fishers would look like a fishing reel, just a spinner and one very long tongue. They'd be bigger than normal itzu and as black as solar cells. Fishers don't pay matter taxes, they are a city unto themselves. But fishers must protect themselves from being gathered by other fishers.
Movers are a fifth profession.
They move things from here to there. Plants are a sixth profession. They gather light and convert it to chemical energy, to be used by other itzu. Travellers are a seventh profession. They shoot out into the universe in all directions at about the speed of light, hoping to find a solar system that doesn't have any itzu yet so they can build a world to their liking.