The Word of Blake took over the Circinian Federation and had extensive power over the Taurian Concordat, gained through technological assistance and gifts of things like Vendetta. They also dropped space rocks on the Taurian capitol, pinning the blame on the Federated Suns to send them haring off a spoiling attack.
They had some degree of power in the Magistracy of Canopus, though far less than they did over the Concordat, and less than the Blakists were hoping for.
In addition to that, they had hidden Periphery staging bases and some kind of relationship with the Hanseatic League. That may have been strictly commercial, but perhaps not.