I was thinking at one point of a Kamen Rider series based around martial arts.
I know that technically, it could be argued that all Rider shows are based around martial arts, since the fight scenes are all choreographed hand-to-hand fights performed by trained stuntmen, but I mean a show with a story that actually is built around ideas and themes from martial arts movies (secluded temples out in the forest, chi power, rival schools, etc.).
The idea I had - and this is pretty much just a skeleton, because I haven't really bothered doing much with the idea - is that there are...let's say 3 different schools of martial arts, located in secluded temples, dating back to ancient times. These schools exist to protect humanity from demons (i.e., kaijin), and they developed the Rider powers with ancient magic as a means of giving them an edge against the demons they fight. Thus, the show would have 3 main Riders, each one representing a different school/temple, and presumably each with a different fighting style. (Maybe the main Rider uses an Aikido/Karate hybrid, while the secondary Rider uses Dragon style kung fu, and the third uses...I dunno, Tae Kwon Do?) The setup for the requisite Rider fights would be the tendency martial arts practitioners sometimes have of assuming that whatever style they practice is "the best," and so each of the 3 Riders, in addition to fighting kaijin, would want to prove the superiority of their style by beating the other two. (Essentially, it's the standard kung fu movie setup of "You bastard! Your kung fu is weak! Now fight me!")
I also thought a cool twist for a little way into the series would be to have it turn out that the Rider powers actually come from demons that have been sealed inside the 3 Riders' belts, and if a Rider takes enough damage in battle, the demon takes over. This would also be the initial mid-series upgrade for each character - a secondary, scarier-looking Demon Rider form that has more raw power, but is completely feral and crazy dangerous. Everybody's ultimate form would be a form that lets them access the raw power of the Demon Rider form, but stay in control of themselves at the same time.