Other than it will revitalise the conduct of relations between factions and pirates there seems to have been nothing posted about the second expansion. Without any clues as to the direction that will be taken, suggestions might fail to be relevant at all, however here are a few more!
One of my complaints about the current AI is that it prioritises the relations % over good strategy, which can lead to the conquest of planets far from its core worlds, which are then of limited use and complicate AI fleet movement. A heavy penalty for the possession of worlds that an AI covets- or which it used to own- might correct this flaw?
Another aspect of this focus on relations % is that the AI is entirely hostile to the player at the start, but should the player survive this dangerous beginning it is possible to win almost by manipulation alone. A penalty to the player for holding worlds that the AI wants might help the latter. How about a xeno bonus for same faction type to help establish relations at the start?
If culture is to be made more important, how about adding a logistic penalty for ships out of culture? To avoid constant checks and a penalty on CPU time, there could be a periodic supply check. Add an option for a player to take a scheduled check early and you have a simplified supply system. Then other players have another spy objective....
The best policy is to take your enemy intact- why not be able to capture structures of the same type as your own, rather than destroy them? Why would TEC players destroy TEC trade ports if they can capture the planet? This might require an ability to inhibit scuttles, perhaps a new ability for siege frigates?
Slight modifications to jump time by type of planet might help to make strategy more complicated. However, for a real ambush you'd need at least one type of gravwell with reduced LOS. Also, it might be useful to have a type of gravwell that acted as a natural phase inhibitor. The possiblity to combine both would create ambush sites.... the pirates might like to establish their base there, rather than on an easily discovered fortress asteroid.
