Batch construction at shipyards: Doesn't save time but allows you to build a fleet of ships and eject them together. Rules of one ship per turn still apply-the only difference is the ships are launched in waves. That way you can set a rally point without worrying about lone ships getting intercepted by enemy fleets!
Espionage system based on the intrigue system in crusader kings: An agent's chance at completing their mission (tech theft, sabotage, etc) increases if the planet is unstable. That means that if the planet is unhappy (or feeling the influence of your culture) you have a greater chance of not getting caught. You could also assassinate important people to further destabilize the planet or start wars with a false flag attack (although the civilization you're framing has a chance to smooth things over if they're good diplomats)
More UP stuff:
Vote to condemn another civilization (must not share your dominant ideology)
the chance to influence votes before each session via diplomacy. Right now it seems like the votes are completely random and the AI regularly votes against their interests.
The ability to mothball ships. Mothballed ships cost less to maintain but slowly lose exp/veterancy points. They would also be highlighted on the diplomacy screen to make them easy to identify for trading purposes. In addition, the shipyard could automatically design export models that are weaker than your regular ships.
Starbase improvements: More than one way to upgrade starbases-instead of a constructor you can use planets to sponsor a starbase and upgrade it overtime. Note tat planets cannot sponsor both a shipyard and a starbase! However starbases incur an additional maintenance penalty if they are not within your cultural borders-mining behind enemy lines has its costs.
Building small ships on-planet. You start with the ability to build tiny ships without a shipyard. Logistics technologies would allow you to build bigger ships on the planet's surface, but the largest ships (and perhaps ships with certain modules) would always require a dedicated shipyard.
Terror star 2.0: This time terror stars would be more customizable and a lot more flexible! You could customize them to intercept enemy fleets (with fighter bays and the latest in hyperdrive technoology) support your own fleets by vastly increasing their range and coordination, wipe planets clean and re-colonize them (with a permanent reduction to planet quality), or use an accurate but slow charging weapon to obliterate enemy solar systems (no more waiting to destroy a star when you could capture it in half the time.) And of course terror stars wouldn't be bannable in the UP until at least one has been built and used!
Different kinds of wars: Another idea I borrowed from a paradox game. You wouldn't need a cassus belli to declare war but having one would significantyl reduce approval and diplomatic penalties. Say an enemy has built starbases in your territory and is mining thulium that should belong to you. Instead of having to declare "total war" (what we have now) ad be prepared for a long war of attrition, you would get to pick from a list of availble cassus bellis (in this case, "remove starbases".) This would limit you to destroying starbases in your territory-invading a planet would escalate the war and give you a significant approval penalty. Once you have completed your objective the enemy would have the option to unilaterally end the war (if they're weak) or escalate (if they're stronger) with no approval penalty. Other cassus bellis would include liberating recently captured planets, trade wars (would boost your trade routes and weaken theirs) and enforcing UP resolutions.
