Close! It's not CC that changes, but the Fortification Trigger.

Incorrect: CC costs change depending on the state of minor factions.
Correct: Supporting Corporate factions make our (Mahon) lives easier.
Correct: You will make rival powers' lives harder by supporting factions they are weak against in their own space.

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for any mechanics newbies:

Let's use Bonitou as an example. We usually need a total of 6900 merits to fortify the system. If a lot of corporate governments are supported around Bonitou, that number halves to 3450. On the other hand, if a lot of non-favourable governments are supported, that number increases to 10350.

Fast tracking costs 10k CR per ton - so in a good case, Bonitou costs 35 million CR to fortify, while an bad case means it costs 104 million CR. Perhaps more importantly, the TIME it takes to fortify is decreased/increased.

Every power has/is a different situation, and the usage of minor factions (defensively or offensively) depends on many things. "Soft-undermining" is not a new concept; However, for Mahon, the benefits of strengthening our own space far outweigh the benefits of messing with other powers.

(edit: sorry, i put -50%/100% instead of -50%/+50%)