My idea for overcharging: A system can be overcharged by up to four bars or the half the current maximum rounded up, whichever is less (so you can't have a level one weapon room overcharged with a Burst Laser mk III, for example). While overcharged, it receives the appropriate benefit (an increased heal rate for medbay, for example). However, while overcharged by n bars, it takes damage as though it is under attack by n units. Further, while overcharged it cannot be repaired at all.
Second idea: this would be something unique to a ship, similar to the Fed Cruiser artillery beam. A system, upgradeable to a maximum of 5 units. You can spend a unit of fuel to increase your reactor's output by 1 energy bar until the next time you jump.
Third idea: Another one-ship thing. The ship has, instead of one single weapons room, three or five single-weapon rooms, like the flagship but connected to the rest of the ship. Each of these is separately manned, and the first one is powered separately as well, though manning weapons gives a better-than normal benefit on the secondary weapons. The first weapon room is limited to laser or missile weapons, but gives a bonus, depending on the weapon. Heavy Laser, Mk I and II would do three damage apiece. Heavy Pierce and the Crystal lasers would pierce an extra layer of shields, Heavy Ion would do 4 Ion damage, Burst Lasers and the Pegasus missile launcher would have a larger volley size, etc.
Idea the Fourth: The Texas Theory of Warfare: Make it Bigger: Capital Ships. In a new campaign set some time after the events of the first, you are commanding a Federation dreadnought in an assault on a hostile enemy.