Configurational-bias Monte Carlo (CBMC) simulations are carried out to investigate the structure and phase behavior of self-assembled monolayers consisting of equimolar alkanethiolate mixtures chemisorbed on the surface of gold nanoparticles. The simulations probe the effects of variations in the chain length, nanoparticle curvature, and exchange of alkanethiolates between nanoparticles. The TraPPE-UA force field is used for the alkanethiolates, whereas the nanoparticle is represented by gold atoms placed on the surface of a sphere. CBMC identity exchange moves are used to enhance sampling of the spatial distribution of the different ligands and to ensure that thermodynamic equilibrium is reached. At a temperature of 298 K, mixtures differing in length by four methylene units exhibit some degree of local segregation. In contrast, the hexanethiolate/tetradecanethiolate mixture yields Janus-like arrangement when the ligands are confined to a single nanoparticle but global demixing when the ligands are allowed to distribute between two nanoparticles.