First off, fantastic game! I have been waiting for a good real-time 4X strategy game for a long time. Last one I tried was Hegemonia and was not executed very well, mainly the very small fleet battles. This game is amazing with the large fleet battles, vast galaxy, and the large amount of building options you can have for planets (planets look and feel like developed planets rather than just another resource node). That said, I have a few ideas for additions that could be added to the game that would turn this game into a real legend.
First off, capitol ships. I didn't enjoy the part about being able to build every capital ship in the game right off the start with zero research first being done. Capital ships should become accessible after you conduct certain research, like for the Advent's Haylcon, make it available after you complete research on Hangar Defense, Burst Modulated Lasers 2/2, and Improved Beam Emitters 2/2. No actual prototype research, rather once you complete x and x research, they become available. However, I do greatly enjoy the idea behind having your first capital ship free and think it should be expanded upon. For example, your first capital ship is labeled Flag Ship, an idea I have is to instead of starting the game with a free capital ship, since you won't be able to build capital ships right away, is to rather every race starts off with a blank, unique type of capital ship. It's not as strong as the other capital ships, but it is strong enough to hold off a few pirate ships in the beginning. The ship starts off completely blank, nothing on it and instead you choose from one of three lines of how to specialize your ship and the first point sets up your ship from there. There would be three lines, a combat type, special abilities type, and a faction unique line. The ship should would then grow in strength from leveling from that particular line and after certain research has been conducted, could be upgraded in a modular fashion. The faction unique lines would go down the lines of say the TEC unique flag ship line would be along the lines of economy and building bonuses, while in the gravity well of a planet a passive increase in resource generation and production is experienced by that particular planet. The Advent could get something like combat aura abilities, while the Vasari could get something along the lines of fleet movement bonuses, for example the ability to have a fleet make a phase jump that would normally require two or three phase jumps to reach a target, a limited range wormhole style of travel.
Lastly, I think a more in-depth diplomacy system would do wonders. Have a system where you you can trade certain technologies in exchange for a few ships, resources or other technology. The trick here would be the certain technologies, when traded with a different race than you own, would yield advances into hidden research topics due to the blending of technologies. For example, if the Advent gave the TEC some beam technology, all TEC ships that had beam weapons would then emit a purple beam (versus the orange of the TEC or blue of the Advent) with slightly more damage and range than before, not enough to compete with Advent damage but an upgrade, and can research ways to increase rate of fire for all beam weapons. Also if the TEC traded some of their economic technologies with the Advent, the Advent would get cheaper mining facilities.
These are not what I believe should be, rather just examples conveying my idea for new game mechanics. Please feel free to comment on or add to my ideas. Oh and again, fantastic work on this great game Stardock. I look forward to seeing the experiencing the other two chapters when they are developed.