Capturable Objects
The idea is to create a sort of "capturable base." I think this would work really well in core. Have a core that's tough to reach from the outside. Players then work their way into a base and convert turrets and laserbeams to their color. So instead of taking a few shots at a core and having it repaired in your absence, an enemy must defend/repair their core AND their base assets.
Depending on gameplay testing it might be necessary to strengthen turret and laserbeam possession to increase their value. One way to do this would be to require several more hits to the turret or lasers after it has lost its health but before it changes possession. In other words, the steps for converting a red turret to blue would be:
1. Shoot at a turret to kill its health which keeps it alive and firing.
The turret is now dead, but is still possessed by the red team.
2. Continue shooting at the turret for a few more seconds in order to force its possession to change to neutral.
The turret is now white and neutral, and no longer belongs to red.
3. Repair the turret for a few seconds to capture possession.
During this step the turret does NOT gain health, but gradually changes color from white into blue (or some other visual effect occurs). After this step the turret is now blue but has no health.
4. Repair the turret for a few more seconds to boost its health.
The turret is now fully blue and fully healed/active.
tl;dr Alive - Dead - Neutral - Dead - Alive. The variables (number of hits to destroy, to repair, etc) of that would need to be modified depending on testing I'm sure.