So here's a little something I've worked out. It's long been my impression that you could essentially take the first four villain bosses and assign each one an alchemical element. Observe:
Giovanni is a ground-type Gym Leader when he's not being a Team Rocket boss, so his element is earth.
Archie is a pirate who wants to expand the sea, so his element is water.
Maxie is the leader of an organization called Team Magma, who likes volcanoes, so his element is fire.
Cyrus was trickier, but in broad strokes, his element seems to be air. Think about it: his organization's headquarters are on a mountain face, his plan comes to fruition on top of a mountain, his star pokemon is a giant crow, and he's even named after a celestial object. There's also the fact that air, in certain circles, is associated with intellect at the expense of emotion (which is basically what Cyrus believes in).
So with that in mind, try applying them to any other form of media that has those four elements involved....( See the examples I've got )
Yeah. There may be many more options, but I can't think of any more that I can bring to make sense.