quadruple battles!
Ok, this is probably never gonna happen because it would make the gameplay too complex, but what about a system where you get to choose how your Pokemon reacts to oncoming attacks?
Usually when a Pokemon launches an attack, the attacked Pokemon is just.. stationary. And with some moves there's a predetermined chance the Pokemon will miss, or the attacked Pokemon will dodge, but nothing much else. There are evasion raising and accuracy lowering moves to help, but it's just not enough. Instead, why not give the attacked Pokemon a chance to react?
What I propose is something along these lines: when an enemy attacks, you're presented with three choices: Dodge, Defend, or Counter-attack.
If you choose to dodge, your Pokemon will try to evade the oncoming attack. Its chances of success at this depend on a mathematical formula taking into account both Pokemon's speed stats, the difference between the attacker's accuracy stat and the defender's evasion stat, and the move's accuracy. The catch is, if you fail at dodging, the oncoming attack's damage is increased because your Pokemon was unprepared to take it. Perhaps by 5% to 10% or so, nothing too broken.
If you choose to defend it's even simpler: your Pokemon braces itself for the attack. The damage then done is calculated based on the attacker's attack/sp.attack and defender's defense/sp.defense and the move's power as usual, but the damage would be reduced by about 10% to 15%.
Counter-attack is like the name implies as well. First your Pokemon get hit, with the attack doing normal damage. Then if your Pokemon is still up, you can select a move to counter-attack with. But, this counter-attack will be significantly weaker than normal. Its damage will be reduced by about 40% to 50%, since it is almost guaranteed to hit the opponent (well, depending on its accuracy and your Pokemon's accuracy).
This only applies to damaging moves of course. Other moves would probably continue to function like normal, since there's a lot of different kinds and many of them are generally unavoidable/defendable. Plus being able to counter-attack any move is pretty broken, even if the damage is reduced. There are also no-miss moves, which would disable the dodge function and limit you to defending or counter-attacking. If either a Pokemon misses its attack, or a one-hit-kill move is about to strike true, the options won't even appear.
It's just a rough idea that I think would probably need to be nerfed down, but I think it'd add a whole new level to the gameplay. It would be nice if they made a spin-off with this sort of system implemented, at least, made for the older fans. ;3