I tinkered for a few hours yesterday, and while I'm far from having a full class yet, I think I've got a workable baseline.
Anima
At first level the Anima picks an anima blast (the base options are air, earth, fire, and water, but you also pick an archetype at first level that might give you a different option). The blast is pretty straightforward, but you learn a variety of techniques -- infusions to enhance attacks, guards that provide defense, and arts that cover the rest of the options.
Some techniques are available to multiple elements, or might be limited to one or two, or might be better with some elements than others. Like, fire can't be used to shove the water the other elements can, but fire can easily do ongoing damage (air and earth cannot, while water can if you've learned to create ice blasts). Earth is great at barriers that stay on their own, while other elements require your concentration if you want to keep up a wall.
At first, you have to spend a bonus action to 'harness energy' which prepares one of your techniques. But you also get a combat poise, which offers a way for you to freely harness energy without spending a bonus action. One poise rewards you if you stay in one place and 'draw upon the root,' while another rewards if you're constantly in motion, 'gathering from the flow.'
At higher levels there are more techniques, more poises, and the ability to learn advanced techniques (like blood puppeting, astral projection, controlling metal or lava, and yes, learning additional elements.) Plus all sorts of other neat stuff I haven't worked out yet.
The archetypes I'm planning are Ardent, Elemental Warrior, and Exalten. The ardent can use their body and spirit to fuel masterful displays of power (think elemental wizard, more like Avatar Roku). The elemental warrior joins the thick of the fight, weaving together channeling and martial arts (this is more like Avatar Korra). The exalten turns the environment around them into a reflection of their will and emotions, and are talented at creating a favorable battleground for their allies (which doesn't really have an analog in the cartoons, but I wanted a controller, a striker, and a leader).
Now I need to spend a lot of time filling out the specifics and making the class choice options fun.