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.