Dead Man's Chest- corsairs were notorious for buried loot, yet all you get for their base is a sinister-looking slightly upgraded asteroid.
'If you do not send them the amount'- another popular activity was to take captives for ransom. If they steal a scientist it might impact research, and industrialist mining, a merchant trade, a celebrity culture.... They were also slave traders, perhaps population could be purchased?
Pirates may have been amoral, but they were also unforgiving, sentimental creatures who mixed gunpowder with their rum, and exacted reprisals for their betrayed fellows. If you destroy pirate ships their price should rise (negative multiplier on bounty), likewise if their ships are destroyed in your service.
They were daring sailors, so their base might have a nearby wormhole, and their ships might be made faster. Unless they were taken unawares, when they might be drunk...
Pirates were smugglers, perhaps they could be attracted by tariffs on trade if these become a part of the new system of faction relations. They took captured ships as prizes as well, though many were refitted for piracy.
