Maybe blender does this already, but I do not know. I have not found out how to make blender preserve existing shape when doing a subdivision.
So I thought about this idea. The existing vertices do not move. But the new vertex extrudes outward along the original normal.
Right it does some kind of smoothing making the model shrink. But if the original vertices do not move, and the new ones extrude. It could preserve it’s original shape while giving it more smoother geometry.
Does blender already do this with some hidden option?