A complex Dyson sphere consisting of three thin coradial shells holding 127 equal spherical stationary planets in a coradial spherical constellation would have several gravitational zones. The structure is inviting for analysis with the inner shell tangent to the innermost point of the planets, the middle shell intersecting the planets at their center (with solid / solid overlap), the outer shell tangent to the outermost point of the planets.
The inside surface of the innermost shell exactly between the planets where the planets and shell have equal gravitational contribution would have a slight gravitational pull directed towards the center of the construct because this position has balanced influence from the shells and other planets but lacks the upwards pull of a local planet. There no lateral gravitation here because of symmetry but stability is neutral so an object that is nearer a local planet will be drawn towards it. Directly under the planet there will be gravitational force directed upwards towards the center of the planet and away from the complexes' center which at this special point are in the same direction. The upwards force is much less than it would be if the planet was by itself due to the influence of the rest of the construct.
The few positions just analyzed were very special. If you followed me well than I can trust the analysis of other points to you as you wish.
Aloha, Charlie
