especially where a number of "assisting" nations are involved. But, let's take just the simple case of HN and one AN - looking at it from a legal standpoint.

You would have to have two charts (one HN and one AN) since the relative civil and military efforts in each of the little boxes are not necessarily the same and are probably going to be different (HN vice AN).

Then, for each of those boxes, we have to ask what law (whose law) applies in each situation. That is positing that the civil effort in each box is ruled by the Rule of Law (but whose, HN or AN ?) and the military effort is ruled by the Laws of War (LOAC), which may differ (again a HN or AN issue).

Pile on a few more nations, Status of Forces and Security Assistance agreements, plus a few different (and possibly conflicting) international and collective charters and mandates, and then we are approaching reality.

Legally, all of this "stuff" is complex.

PS: and now we have a new COIN, Combat Operations In support of another Nation. That definition does translate readily into LOAC terms.