Double skin

Hi I am trying to create a double skin but it will not work if I scale it how I would want from the middle. The idea I have managed with a sphere but when I have 3 booleaned together at different scales it doesn’t quite work, I would like to use proximity 3d or multipipe afterwards to create a double skin structure as the red lines indicate in the picture, In the other picture showing how I am scaling in the wrong way, Thanks for any help in advance

mesh boolean (43.3 KB)

Increase sphere radius instead of scaling: