What are the pros/cons and effects of stirring, either "too much" or "too short", in a French press?  My rule of thumb for steeping is to let the coffee cool down to a drinkable temperature, then serve immediately.

I was going with the thinking that in whatever chemical reaction is occurring during the brew, I would want to accelerate it with maximum stirring.  Particularly when maximizing caffeine?

The video here:

https://en.wikipedia.org/wiki/French_press#Preparation

shows a quick stir only, however.  They mention a range of brewing times.

(side question:  the only reason **not** to stir with a metal spoon is to prevent breaking the beaker?)