First of all there are many types of magnetic anisotropy ( like Magnetocrystalline , Magnetoelastic , Shape and surface anisotropy etc. ) which anisotropy are you interested in ??
All these Anisotropies are additive in nature (with positive or negative sign) , so they may affect the resultant value of magnetic anisotropy.
There is no General result , as anisotropy depends upon shape as well as stress and other factors too But for specific conditions you can ask such question.
That one which will have the strongest/weakest magnetic field on the chosen particular direction (since the difference in strongest/weakest will give you the maximum values). In any way it is an ensemble average and the strength is adding up. You can talk about the magnetic properties taking only one atom and its surroundings too.