Geobreeders is a manga by Akihiro Ito, which was serialized in Young King OURS from 1993 to 2009. It was adapted into two six-episode OVAs, the first being released in 1998 and the second from 2000 to 2001.
The story is centered around the Kagura Security team, consisting of Mr. Taba, our sympathetic mid-twenties hero, Yuka, the genki girl boss who frequently goes by Madame President, Yu, the under-enthused driver, Takano, the glasses-wearing, rollerblading... one, Eiko, the very professional one, and Make, alias Crimson Shooting Star, a gunwoman in a white suit. Their agency tracks down and "deletes" phantom cats that can travel thought electric currents, phase through walls, and take the form of people. One such cat is actually befriended by Mr. Taba, although she is the only phantom cat seen that cannot speak. Her name is Maya.
This series is a bit of a mash-up of many popular anime genres. There's a bit of unwanted harem, with it being Mr. Taba's job instead of his home, loads of action, science-fiction fantasy, madcap comedy and fanservice. Lots of fanservice.
Geobreeders provides examples of the following tropes:
- Action Girl: A lot of them. The only male characters are Mr. Taba and some of the various villains throughout the series.
- Cat Girl: Lots of them. And Catboys too. Maya is the main qualifier.
- Chew Toy: Mr Taba, who gets into more humiliating and demeaning, as well as dangerous, situations than all the ladies he works for.
- Drives Like Crazy: There is that time that Yu side-swiped a missile.
- Genki Girl: Yuka definitely qualifies for this.
- Hero Insurance: NOPE. much of the time, a lot of the damages the Kagura team needs to pay off get drawn out of Mr Taba's paycheck.
- Never Bareheaded: Maki is never seen without her fedora. She doesn't even takes it off while taking a bath!
- Red Baron: Maki Umezaki, a.k.a. "Crimson Shooting Star" (and she would really like you to call her by that name). Her Rival calls herself "Indigo Shooting Star".
- Unwanted Harem: Sort of. Taba is surrounded by women (not always fully clothed either, as the first episode shows us), but only a few of them actually come on to him directly.
- Youkai: The Phantom Cats have a lot of attributes that make them rather demon-like.