YOUNG MAN: My cousin hopes to become a Companion. But I don't think the academy will take her unless her scores come up.
INARA: It was the languages I struggled with. And music, at first.
Companions are a cross between the oriental-style Geisha and the classic courtesan of renaissance Italy -- in many ways, they are the highest ranking nobility of the Firefly 'verse -- when it comes time for a show of power between a high-ranking member of a Core World's administration and a single Companion... bet on the Companion.
The only thing likely to outmaneuver such a woman is The Guild itself -- few companions will knowingly cross Guild Law.