In Rumble we have Straight, Kick and Uppercut modifiers with a single cooldown timer for each. That means that if you do the modifier on any side (right or left), you will still have to wait for cooldown to end to make a new move.
Counter example is how we have Right Hold and Left Hold modifiers, which are considered as separate modifier moves and thus don't share the same cooldown timer. Currently switching between them both is used in some chambering combos for more speed.
I have two interesting suggestions to choose from:
  1. Make Right Straight, Left Straight, Right Kick, Left Kick, Right Uppercut and Left Uppercut modifiers with separeted cooldown timers, so that you can do the same modifier if you are fast enough to switch hand poses.
  2. Add the same effect as a new shiftstone you can equip to buff an ambidexterous playstyle with the same effect but for the cost of a shiftstone slot.
Both implementations will allow for new combos, though the second seems safer in breaking the current balance of the game less (the Charge shiftstone will gain competition with double Straight users, but I also want to see the Charge + this one shiftstone combo).
Softer version of this suggestion is decreasing the cooldown for the mirrored modifier instead of having them completely separated (for example, making it half, so that wait time between Right Straight and Left Straight will be 0,25s instead of 0,5s).