There's Mai-Otome, Mai-Otome Zwei (an OVA series), and Mai-Otome 0~S.ifr~ (a prequel OVA series), as well as various related novels collecting stories that ran in Megami or whatever (there may be some bespoke novels, too, I'm not sure) for both Mai-HiME and Mai-Otome, and a manga series for Mai-Otome as well as the one (more than one?) for Mai-HiME. Plus a couple of vidja games that are set in another Mai-HiME AU (at least the PS2 one is).
Otome is great fun once it gets going. I don't like it quite as much as the original series, but it's very enjoyable in its own right as well as having amusing touches if you've seen and enjoyed Mai-HiME first.