Opposite rep changes
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Not entirely sure what is your question, but I assume you mean how to?
This is controlled by the file DATA\MISSIONS\empathy.ini which contains each faction’s reaction with all other factions. Negative empathy_rate values such as -0.4 mean that a 0.1-unit increase in your rep with this faction will decrease your rep with the other faction by 0.4 units.
As you will see, you can destroy the ships and also destroy the property of a faction to improve your rep with their enemies, and decrease your rep with their allies.
For example in the vanilla game you can destroy a couple of the Police-owned storage canisters near Newark station to improve your rep with the criminals (Rogues, Xenos, Junkers etc). It will reduce your rep with the legals (police etc) too so don’t destroy too many without checking - and please leave some canisters for other players!
If a faction is not listed in a faction’s empathy listing then there is no reaction by the missing faction when you destroy this faction’s ships or property.
Note that aborting a mission for a faction can reduce your reputation with the faction you are working for too if it is in the listing.
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If you mean can you get better rep with a faction by killing its own ships - well I don’t think so, but try if it’s your mod to set the “event = object_destruction” parameter to a positive number maybe?
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Yes it works. Just use positive values here.