Instead of getting larger by orders of magnitude to fill out a galaxy, advanced civilizations get smaller by using nanotech.
Biologic cells as we know them are too bulky, slow, and inefficient. As a result, to expand by orders of magnitudes we would have to take over planets, star systems, and eventually galaxies.
But maybe instead we could convert from biology to computers based on nanotech. By shrinking ourselves we could still expand by orders of magnitudes and not take up more than a few star systems.