The recent replies had me think more about history, and I also had been pondering how I want to handle territory. So here is what little I know on these subjects so far.

Some fragments of history

- There are numerous ancient ruins throughout many parts of known space that belong to a civilization that doesn't exist anymore. There are some remains of bodies on airless moons, and a few depictions on ruin walls that show that it was not a species known to be alive today, but nothing else is known about who they were or what happend to them.

- Another civilization that was known to the Aquatics and Mantises a very long time ago seems to have simply disappeared with no known cause several thousand years ago. Somehow their interstellar civilization collapsed and their systems became more isolated, until eventually Hyperspace routes were no longer updated. It is very likely that some of the planets survived and are still inhabited, but all their systems that were known to the Aquatics and Mantises were later found to have been abandoned a long time ago.

- The Mantises have been in space for a very long time and created a large interstellar civilization. But a few thousand years ago, the civilization sharply declined and fractured, facing the same outlook as the previously lost civilization. But in this case, three large colonies remained in contact with each other for the entire time, even though travel between the systems became very difficult without access to new ships and infrastructure support from the homeworld and other major planets, and updating the Hyperspace routes between their systems became an econokic challenge. It was only when three colonies made contact with the Giants that they got access to Hyperspace charts for all of (then) known space, and the industrial support to resume large scale ship building. By analyzing antique star charts from their old civilization they were able to match some of their ancient systems to stars in current charts, and after calculating new Hyperspace routes send ships to see what had happened to their planets. Some of these colonies had survived for the whole time and are now minor states, but the majority had been found abandoned long ago, with no information of what happened to the populations.

- The Aquatics have been to space since the days of the old Mantis civilization, but though they knew of each other, they had almost no contact at that time. Then Aquatics gained Hyperspace drive technology by reverse engneering some ships they had traded from the alien civilization that mysteriously disappeared not long after, but their limited understanding of Hyperspace navigation restricted them to just a few systems very close to their homeworld for a long time.

- The giants develope Hyperspace drives on their own, and while the construction is quite different from the other main type of Hyperspace drives, it's based in the same underlying principles. When the Giants discovered the remains of the Mantis civilization and shared their Hyperspace routes with them, they started the current age of interstellar society in known space.

- When the Mantises had regained the ability to build ships for long distance journeys in large numbers and access to many more Hyperspace routes, their search for other surviving planet brought them into contact with the Reds, with which they shared Hyperspace drive technology. In the many centuries since then, the Reds have established a very significant number of colonies, which make them one of the four leading species today.

- At some point, tens of thousands of years ago, the Reds had previously been discovered by an unknown alien civilization. The period peristed only as a vague myth in the culture of the planet, but for unknown reasons the aliens had taken some of the Reds and settled them on a cold planet around a red dwarf a considerable distance away from their hoeworld. On the new world they developed a completely separate culture and civilization, and lost almost all of their coloration under the weak sunlight, becoming the Whites. When the Whites were discovered by other species only a few centuries ago, they were already very technologically advanced in fields other than Hyperspace travel, and they adopted new technologies and industries very quickly. While they have estalished only a few colonies so far, they are already one of the more technologically advanced species.

Some thoughts on territory
I tried coming up with some kind of very rough map where the systems inhabited by the various species are roughly in relation to each other, but that turned out to be more complex than I thought. The Galactic Republic and the Federation are both federal republics in which each speciws has their own worlds, but they all can freely move between the system. The Federation only has borders with three significant neighbors, so Star Trek can easily handwave that away. .with 12 species thst that each have several states, knowing who is actually neighbors with who becomes a relevant factor, though. But I still want to also eat my cake and have all 12 species appear in the same places on the frontier, so some clever thinking will be required here.

As by the rules for Hyperspace travel as have been established, arrivial points in a system are quite random, and it takes several hours to go between the jump zone to the inner planets where most colonies and outposts are. Unless you're really unlucky, you will always be able to jump out of a system long before any ships present in the system can get to you. Or even missiles. All you need to make another jump is to have enough fuel on your ship. This means that it is impossible for any fleet to block a system for traffic passing through. So having to go through a system controlled by a different state to get to one of your new colonies would not be a big issue. Not much different than having to go through an uninhabited system. In a way, states would be limited to controlling only the inner system (and with giant stars not even that), while the outer syste, would effecrively remain "international waters", "off the coast". That could actually be interesting. Would be really annoying to have an enemy cruiser hanging out at the edge of the system, listening to all long-range communication (though with encryption of couse) and monitoring the coming and going of any ships. Even if you can send ships to threaten them, they can just jump to safety and be back in a day or two.

However, an important part in the previous part was "having enough fuel". I quite like the idea of super-preheating propellants with fusion power before running it through the sublight engines to create thrust with much better fuel efficienctpy than just burning the fuel normally. I doubt that would produce the speeds to get near the travel times I am thinking of, but that's one of the things were it's best not to explain how it's supposed to work specifically. And since Hyperspace is only another dimension, you still need engines to move through Hyperspace once you entered it. Fusion power famously needs very small amounts of fuel, but fusion-heated plasma still would eat through large amounts of propellant. The important part here is that there's only one type of fuel for sublight and Hyperspace that needs regular refueling.

And those fuel stations are something you absolutly can control. If someone wants your fuel, they have to come to you, where you can wait with your weapons ready. But at the same time, fuel stations are infrastructure that can't run away if it is threatened. Frigates, destroyers, and especially cruisers are designed to have large fuel capacities to allow them to make numerous jumps without refueling. But having access to local fuel stations or not significantly impacts the options a cruiser has. Limited access can mean the cruiser has to constantly go back and forth between the systems it's supposed to show its power in and an allied fuel station. Or tankers might have to be dispatched, which could potentially get attacked by local hostiles before the can get covered by the cruiser. Or worse case, a cruiser might get stuck without fuel to make it all the way back behind allied lines.
And it becomes an even bigger for commercial shipping, where cargo ships often calculate things extremely close and would be stranded if a fuel station refuses them service or is out of operaion. By limiting the fuel capacity of ships (and in Stars Without Number, fuel tanks are a ship upgrade that takes up space and can be destroyed in battle) to maybe three to five jumps, fuel stations become the choke point for interstellar travel. They can be attacked and defended, and they can be destroyed or sabotaged to cripple the defenders, or scuttled to prevent falling into enemy hands.

I think a strategic doctrine that focuses around the possession of fuel stations instead of star systems could be an interesting new approach. Those stations might actually be heavily defended fortresses in themselves and not simply highway gas stations.
Capacity would also be a factor. A station designed to service two light freighters per week to let them make it to the next station might not hold enough fuel for a single cruiser jump.