An elemental system with a circle of aspect superiority: water puts out fire consumes air erodes earth soaks up water. Elemental dice cost an extra die (like with sorcery). During advancement, their value is doubled. If you advance superior element dice against inferior elements, each superior die reduces one inferior die to a 0. Likewise, if you advance inferior element dice against a superior element, each superior element die reduces one of yours to 0. Value reduction does not negate superiority, so if someone advances water and air and their opponent advances fire, water reduces fire to 0 and fire still reduces air to 0. White dice may cancel elemental aspects the same way they cancel green aspects -- they cancel both superiority and doubling, simply removing the aspect from the dice (their face value still counts) and the white dice change the score, as when they cancel green aspects.
Power types, like in D&D (acid, cold, fire, force, lightning, thunder, necrotic, poison, psychic, radiant, sonic): I think this can work for genres other than fantasy, too: projectile (guns, arrows), laser, plasma, voodoo, chi, etc. As with other special dice, you spend an extra die (like with BRS sorcery). You tag a standard die with a power type. A powered Force die negates all advanced Fortitude and Finesse (in addition to acting like a regular Force die), unless that component has an undevastated Fortitude or Finesse trait that is powered with that type (doesn't need to be advanced), in which case it just functions like a normal Force die. Making a trait vulnerable to a power type makes the entire component vulnerable but it gains an extra die of the same type from the bone yard, which must be used for another, "linked", trait in the same component. If the vulnerable trait or the linked trait is devastated for any reason, the other one is as well (this reclaims the extra die and should help prevent grinding). Force of the type to which a component is vulnerable damages one extra die in that component. After the attack is resolved, if the vulnerable trait has been devastated, the component is no longer vulnerable to that type of Force.
It seems like powered Force and vulnerable traits are more powerful if there are a lot of choices, because it's harder to defend against them (or gain advantage in the case of vulnerabilities), so groups would probably want to limit the number of power types to something relatively small (like 4 or fewer, maybe).