To understand and predict the adsorption behavior of proteins at high surface coverages, an accurate description of lateral interactions among adsorbed molecules is imperative. We model protein adsorption as the formation of an ordered array of charged particles at a surface, considering both protein-protein and protein-surface interactions within the array. Energies are calculated as a combination of electrostatics, based on the solution of the linearized Poisson-Boltzmann equation, and van der Waals interactions, evaluated by pairwise additive summation. A method is developed for the construction of adsorption isotherms on the basis of a Gibbs surface excess approach. The sensitivity of the system energetics to parameters describing the protein, the surface, and the solvent is assessed, and results indicate that double-layer screening in the electrolyte medium plays a predominant role in the adsorption process. Theoretical isotherms are generated for a spherical approximation of lysozyme which show trends that are consistent with experimental measurements. The model predicts the coexistence of multiple states of adsorption for certain conditions. Multiple equilibria in the theoretical isotherms provide possible explanations for protein adsorption phenomena such as the increase in surface coverage at high ionic strength and the appearance of irregularities in experimental isotherms of some proteins.