Well, humanity would have claim to eight straight off unless you count Pluto in which they'd have nine. So I figured the Cassadrian system would just be a little larger, with a massive star. They'd just lay claim to all of it whether they have any stations or people on every planet nor not. (Similar to how the world claims celestial bodies today) But I'll lower the number a little if you'd like. It'd just mean they have a smaller solar system then I originally planed.