When considering light scattering from a sphere, the ratios between the expansion coefficients of the scattered and the incident field in a spherical basis are known as the Mie coefficients. Generally, Mie coefficients depend on many degrees of freedom, including the dimensions and electromagnetic properties of the spherical object. However, for fundamental research, it is important to have easy expressions for all possible values of Mie coefficients within the existing physical constraints and which depend on the least number of degrees of freedom. While such expressions are known for spheres made from non-absorbing materials, we present here, for the first time to our knowledge, corresponding expressions for spheres made from absorbing materials. To illustrate the usefulness of these expressions, we investigate the upper bound for the absorption cross section of a trimer made from electric dipolar spheres. Given the results, we have designed a dipolar ITO trimer that offers a maximal absorption cross section. Our approach is not limited to dipolar terms, but indeed, as demonstrated in the manuscript, can be applied to higher order terms as well. Using our model, one can scan the entire accessible parameter space of spheres for specific functionalities in systems made from spherical scatterers.