Let's take flame and water for an example and imagine their E is a dash. So if both players use the move at the same time then a clash animation will happen where the player with flame has flame effects towards his side and water user has water effects towards his side making the clash look cooler. They have to click certain keys like Z J K R T F and they have 5 seconds, so whoever wins the clash by then or has the majority meter will get the damage from their move.
Same way for demons. Let's take temari and arrow here. Arrow user uses his single arrow and temari user uses his ball at the same time, the camera will only zoom in at the temari and arrow, where the clash happens again with the temari and arrow are shaking vigorously and the players are clicking keys. The one that comes victorious gets their damage in. But you cannot combo extend with that move (if it is an extender), it will mix with the arrow or temari and hit the other player causing damage 2x than the normal move and a knockback.
But these clashes could happen very frequently if both the players just keep using the moves at the same time. So to prevent this, after the clash there will be a cooldown for clashing for both players. (About 40 seconds). So if the flame and water user uses their E at the same time, they both hit their move in and get knock backed together and if the arrow and temari user uses the arrow and temari at the same time, they both can perfect block each others move if they want or get hit ig.
Not all moves are compatible with clashes so some would be hitting each other at the same time or priority idk however higo decides to make the moves. But only certain demon arts and breathings clash. This is to add on to little intensity in the PvP.
IF there are ultimates, they can clash too. But like I said not all are compatible. So if 2 ultimates which are NOT compatible to each other use their ult at the same time, it's cancelled out for both of them. But this is only if they use it at the EXACT same time. If one uses the ult before atleast 0.5 seconds earlier too then theirs hit. I think to do this, there should be different priority values increasing each second in the move scripts. So if the priority values match then the cancellation or clash happens but if one is higher then that one hits and the other player's ult cancels out.
This sounded cool asf in my head so I thought to put it in. 
This is easier said than done but I just wanted to put this suggestion here.

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