Resolution for overlapping sounds when guns are fired at close range

I’m trying to create sound effects for a TPS game.

The sphere represents the sound emitted by the player,
and the cube represents the sound emitted by enemies.

Both guns are using the same sound cue.
When engaging in a firefight at close range where attenuation isn’t significant, the overlapping of the two identical sounds creates an unpleasant noise.

I think one solution could be to differentiate between the player’s and the enemy’s sounds, or apply effects such as a low-pass filter to mitigate the overlap, or adjust the pitch. However, it still sounds unpleasant with just a low-pass filter.