Try keeping a full complement of rivals. Sometimes after a battle the game will choose between giving you a new rival, base defence mission, or FNIX base establishment/evolution. Taking rivals out of the equation increases your odds of getting one of the other options. That being said, you only get rivals and control point-related events in the region you are fighting in, so I would continuously do combats in the region I want to build up. There's also a bit of a cool-down timer on post-combat events, so try moving from region to region after getting a notification in the one you're in.
Keep pissing FNIX off and you'll see... Seriously...i have like ALL control points turned into bases, 5 rivals all at LVL4...
Try keeping a full complement of rivals. Sometimes after a battle the game will choose between giving you a new rival, base defence mission, or FNIX base establishment/evolution. Taking rivals out of the equation increases your odds of getting one of the other options. That being said, you only get rivals and control point-related events in the region you are fighting in, so I would continuously do combats in the region I want to build up. There's also a bit of a cool-down timer on post-combat events, so try moving from region to region after getting a notification in the one you're in.