Can you stir a pour-over? Can you stir during a pour-over brewing process, or are you really just meant to let it sit?

I ask this because not all pour-over filters are created equal, and some work better than others. 

Factors do include:

a. filter shape (flat-bottom, conical, combination of the two), b. filter media (steel, paper, cloth), and;
c. grind size of the grounded beans.

Usually, when it comes to drip speed, you can just adjust with grind size, try to match it to filter type, follow a decent technique in water pouring to agitate the grounds, and you'll be fine.

But is the purity of this method best left to water and gravity? Or has anyone ever stirred the coffee slush at any point during the brew process to favorable results? 

I'm open to any answer really. I would very much like to hear answers from a practical standpoint (i.e. Will stirring make the coffee brew faster? Taste differently?), as well from a theoretical standpoint that Illustrates the pour-over for what it is meant to be, as a zen-like, artisanal experience. 

I do enjoy the process very much, so I'm really just curious if stirring has ever been a part of it.
The short answer is yes you can stir pour overs and it can be useful but generally not recommended. 

The primary use for stirring pour overs that I have seen is a very light stir to jostle grounds that have stuck to the brewing methods walls. The slight stir at the maximum volume of water in the filter makes sure that as fluid drains grounds stay in the slurry of water and are evenly extracted.