A civilized species uses one star at a time. Some like things quiet and aesthetic with very few visitors, maybe they go full Kardashev Type II and invite everybody to come build a habitat and back up the biomes from their homeworlds there.
Various big space opera plots:
• A stellar stream cut off from the galaxy for aeons reconnects, and it contains a multi-system civilization. An expansionist empire is one kind of problem; a peaceful civilization that has different rules is another one.
• A rebel group is rescuing populations from a world whose dominant faction is expansionist and hiding them and copied biomes in a Type II system.
• An intelligent civilization on a water world will never get to space. Contact them anyway?
And of course there are all the personal-scale plots that can go on in any space opera setting. #bulldogsrpg could be a good system, though the setting would need meddling. http://www.galileogames.com/bulldogs/
This means that the 4X narrative is very different in that universe: galactic consensus is that you live within your means, and any colonists have to be very stealthy. No expansionist, colonialist interstellar empires! Trade is all between and within the well-known civilized systems, unless you’re a rebel.