The rule of thumb I tend to use in my head is that because of this communication and synchronization overhead, total output (in terms of impact) of an organization tends to scale not with # of people, but more like log(# of people).
That's at a well-managed company - with mediocre or poor management it can be more like log(log(# of people)), or "O(1)" (total output remains constant no matter how many people join), or total output can even decrease as the organization grows.
I'd think there is a point where it inverts, too: There is some number N such that the amount of work you can get done with N people is more than you can get done with N+1 people, and it keeps going down with any subsequent person you add. The Mythical Man Month talked about this. At some point, the extra communication overhead spent to sustain person N+1 costs more than the marginal extra output of that person.
Yeah, I meant to cover that under "total output can even decrease as the organization grows" but I guess it got lost in my tortured sentences. Though maybe you mean this is the case even under good management (or perhaps that "good management" gets harder and harder as the organization grows).
iirc, mythical man month doesn't say that output of n > n+1 permanently; it says that you temporarily lose productivity until everyone is brought back up to speed. It becomes an effectively permanent loss if you're using the strategy "the later it is, the more people you throw at it".
But if there's no continous stream of newcomers, or rather sufficient gaps between hiring, then more man-hours does (eventually) produce more output.
That's at a well-managed company - with mediocre or poor management it can be more like log(log(# of people)), or "O(1)" (total output remains constant no matter how many people join), or total output can even decrease as the organization grows.