If I were to construct an air core transformer with multiple secondaries. Would the magnetic coupling be better if the primary was wound around the secondaries or the secondaries positioned around the inner primary. I'm thinking it wouldn't make much difference.
The magnetic coupling of such coils is best when primary and secondaries are wound alongside, each wire tight to the other. The outer form is near to irrelevant. This is called a bifilar winding scheme or bifilar coil.
Three or more cylindrical or planar coils have the disadvantage there will be additional space between the windings.