Ah, power note. That's the proper term. Through further experimentation (and luck), I was able to answer my question.
What I was attempting to ask was if you encountered a power note that you already have equipped, perhaps already upgraded, if picking up the weaker power note would upgrade it. As an example, holding a Turret 2 and finding a Turret 1 after a boss. My thought was that picking up the Turret 1 would add to the level of the equipped Turret 2, making it a Turret 3... Or something of the sort.
Unfortunately, picking up a Turret 1 with a Turret 2 equipped will overwrite it to a Turret 1. Something that isn't described to the player as it is with another power note.