Just a couple of thoughts I'm putting out here while I'm thinking of it. #2/3/4 in particular might have serious AI reprogramming ramifications (not my area of expertise) so design may be already too far along to implement that. If so, put it on the shelf for an expansion.
1. Galaxies/Maps with spiral arms. The arms themselves provide galactic boundaries, so hyperdrive (which apparently doesn't work outside the galactic boundaries) cannot drive ships from arm to arm - you have to go to the "armpit" to cross over.
2. I've seen elsewhere folks refer to the stargates (linked to space stations) as providing "highway" concepts for trading vessels.
This could be expanded or recast as "wormhole technology" to allow fast or instantaneous travel for ships, perhaps with tonnage limits (maybe also researchable). These may allow passage through the "intergalactic" space between spiral arms, but in any case would introduce the capability of establishing "beachheads" in the rear of opponent space. Using them to provide interior lines of communication/logistics/travel within your empire (or to empire outposts) is another use.
Whether the wormhole established would be a permanent fixture or tied to some structure that could be destroyed (or scuttled) would affect the strategic and tactical effectiveness immensely.
The position on the tech tree for basic stargates should be early, since they do predate hyperdrive, but easily/cheaply built ones and the capability of handling massive ships (or fleets) should be quite a bit further out, and use of these (outside of invasion, but in someone else's space) might also require serious diplomatic skills, too. (Thanks, Lord Kona!)
A nerf for balance might require weapons &/or shields to be powered off for transit.
3. Tied into this would be the concepts of stealth &/or cloaking in order to sneak into enemy territory to use these on the offense.