Then there is the ultimate influence equalizer: war. Find what alien is your planet stealer, take some systems away from him while being especially vigilant in destroying influence resource starbases (as well as the standard trashing of military, economy, and morale resource starbases). Your base influence is determined by adding all of your systems together and modifying it at various levels with tech, resources, social projects, culture starbases and so forth. Reducing the size of your rival's empire while increasing the size of your empire helps alleviate the base influence problem at its source. Oh, and be sure that you not only destroy the resource starbases in the war, but claim them for yourself. After a healthy little war that bags the problem starbases and snags a planet or three, force concessions out of the poor alien at the peace talks. If all goes well, the influence advantage over you will be eliminated and you will gain an overall influence that can effect every alien on the map with your greatness, instead of them walking all over you.