Consider the rigidity of bar-joint frameworks in 3-dimensional space that are constrained to lie on a union of spheres. It is well known that rigidity on a single sphere is equivalent to Euclidean rigidity and this equivalence extends to the case where the spheres are concentric. We consider the case when the spheres have distinct centres and give coloured sparsity conditions, analogous to the Euclidean case, necessary for a generic framework on the union of two spheres with different centres to be rigid. We show that these conditions are not sufficient in general and add additional conditions which we prove are sufficient in a special case.