No sorry, I don't think that the construction of such a closed surface is possible. You got me here though since topology is my weak area and I cant find a good argument to back it up. All I can say is that if such a surface was possible then we would argue that any two charge densities are equal. Take for example a surface charge density ##\sigma_1## that is defined on the xy-plane (z=0) and another ##\sigma_2## on the plane z=5. Using your argument we can conclude that they are always equal.