Spin-crossover (SCO) solids have been studied from magnetic and structural viewpoints under the form of powder, single crystals, and nanoparticles. Recently, an important progress made in chemistry allowed the design of spin-crossover nanocomposites, combining the properties of two types of spin-crossover solids having different properties, for example, different transition temperatures, ligand fields, etc. In this work, we sketch theoretical investigations based on an elastic description of a SCO nanocomposite, aiming to reproduce the experimental results of literature which exhibited two-step and even three-step spin transitions. Our results not only reproduce the experimental features but also allow a better understanding of the interplay between the elastic and electronic structures of the two components of the SCO nanocomposite. The obtained data offer serious possibilities of extensions to several configurations of nanocomposites according to the shape of the lattice and the relative sizes of the two components under study.