I was taught that the shape of the stop sign is octagon (and yield triangle) because you can recognize the shape from behind. The main road doesn't need to have the diamond priority sign. You know you have priority if the you see the octagon or triangular shape on adjoining roads.

Not sure I understand what you are saying here...

Imagine driving towards an intersection. There is no sign telling you if you have priority or not. There is a red car coming from the right. Then you notice that the red car has a stop sign in front of him (you recognize the shape). You infer that you are on the main road and you can ignore the right-hand rule.

Sorry, I understood what you meant, just not what the relevance was. What you are saying applies, and applies universally (regardless of whether there also exists multi-way-stops).

That there is no need for supplemental signs I guess.

Either you have a regular stop intersection, in which case there are octagonal stop signs on the roads that do not have priority. No supplemental signs needed. A driver stopping at the stop sign knows that when the intersection is clear he can drive. If it's a 4 way and he's turning left, he may have to yield to a driver on the opposite road, depending on the local laws (In a right hand yield priority the car turning left yields to the car in the opposite road).

Or it's a multi-way-stop (which is rare) in which case all roads have the supplemental sign. None of the roads have priority and all drivers can do to resolve deadlocks is be careful. All the supplemental sign does is inform drivers that OTHER drivers will also stop. It just removes the ambiguity we talked about above - where a driver at a stop sign might otherwise think he can't drive until the intersection is completely clear.