I have a loose idea in mind where the story starts at a familiar place:
The PCs intercept a distress call from a nearby ship. Once they investigate, they find a damaged freighter floating in space. They breach it and find damage everywhere and bodies strewn about. As they investigate further they find a number of crude forms of android and they have taken over the ship and killed its occupants.
Later in the campaign, the investigation would lead to one of the Cults mentioned in the Starter Kit and how they plan on releasing xenomorph entities throughout the core systems.
I'd like to limit the amount of xenomorph activity and really make them a threat later on. I like the idea of exploring the entire universe and not just the Weyland-Yutani/xenomorph thing.