I did this one time without even trying in another game. In my current game I am trying to get a race to flip to me. They have some planets inside my spheres on influence. I have built several buildings for influence like that restaurant or whatever it is that can be only 1. I have all the influence stuff on nearby planets and I have researched a fair way up the cultural tree and in 1 case I have 5 influence starbases around 1 planet and all upgraded ALL the way up. Still they won't flip to me. I am spending 70 bc on inflitration so I see what they are up to. My planets near them are at 100% happy too.
What am I missing? What do I need to get planets to start flipping to me?