By means of a combination of atomistic and density-functional theory calculations it is shown that small changes in composition, achieved by introducing a small percentage of impurities in a matrix nanoparticle, can have drastic effects on its structure even for quite large nanoparticle sizes, containing up to a few thousand atoms. This has the consequence that the nonscalable regime in binary nanoparticles can extend to significantly larger sizes than in single-component nanoparticles. Specific examples are given for the systems Cu-Ag, Ni-Ag, Co-Ag, Ni-Cu, Co-Au, Ni-Pd, and Rh-Ni.