How about a Capture the Relic mode where a non captureable gravity well spawns a capturable prize on a similiar time frame to when pirates spawn.
This prize can be picked up by a colony ship, and if carried to the capital world of a faction, results in a hefty bonus (resources, money, planetary or tech bonus (similiar to planetary relics), pirates immediatly launch at all other factions, You get the idea. It's worth capturing.
However there's a catch. The ship carrying the relic moves at a slower speed (I suggest half) and has reduced or zero firepower. Making it easy to intercept, it has to be escorted...
Fun?