Hi Drumheller,
If by “box spring” you mean a non flexing slatted foundation or even a solid surface foundation then this could work as long as the combination was stable and one didn’t shift or move on top of the other. If by “box spring” you mean a base with actual springs inside it that flex then I wouldn’t go in that direction because it wouldn’t be as stable as a firm non flexing foundation and could tilt from side to side. I would also want to know that the bunkie board that was directly under the mattress was suitable for use under your mattress (that the slats were close enough together) and met the manufacturer’s criteria and if it was a solid surface that you were comfortable with any additional risk of using a less breathable base under your mattress (see post #10 here).
Phoenix